Tutor MathsGuru: Ask me for your burning Maths questions!

[YLH88]

Hi all,


Need help with the below questions :? :

1)At 11am, a van set off from Town P for Town Q while a car set off from Town Q for Town P.
At 4pm, the van and the car passed each other.
4 hours after they met, the car reached Town P but the van was still 180km away from Town Q.
Find the distance between Town P and Town Q.


2) Greg counted the number of cars, vans and motorcycles parked at the multi-storey carpark.
There were 5/9 as many vans as cars.
1/4 of the number of motorcycles was 36 less than 1/5 of the number of vans.
After some cars left the carpark, there was an equal number of cars and vans.
Given that there was a total of 480 cars and motorcycles at the carpark at first, how many cars left the carparks ?


3) The capacity of a mug is 1375 ml less than the capacity of a jar.
The capacity of a cup is 1/5 that of a mug.
4/9 of the amount of orange cordial in a dispenser was used to fill 3 cups and 5 mugs completely.
3/5 of the remaining amount of orange cordial was used to fill 2 jars completely.
Find the difference between the capacity of a jar and a cup.

Thank you!

[benorito]

Dharma:

firebird:

Dear maths guru


Please help me on the following maths:



2) At 9am John was cycling from Point A to Point B. At the same time, Mary was cycling from point B to point A using the same route as John. Cycliing at a speed of 4km/h faster than Mary, they would pass each other 300 meter away from the mid point.

a) What time did they pass each other?


a) Difference in distance travelled by John and Mary = 4km/h x T
T = 0.3km x 2/(4km/hr) = 3/20 hrs = 9 mins
Time they passed each other => 9.09am

Dharma,

Can you tell me why you must multiply the 0.3 km by 2 ?

Thanks

[Vanilla Cake]

YLH88:

1)At 11am, a van set off from Town P for Town Q while a car set off from Town Q for Town P.At 4pm, the van and the car passed each other.4 hours after they met, the car reached Town P but the van was still 180km away from Town Q.Find the distance between Town P and Town Q.

11 am (set off) to 4 pm (passed each other) -> 5 h
So, the van and car took 5h for the whole journey.
1h -> 1/5 of the journey together

Car
5h + 4h = 9h to complete the journey
1 h -> 1/9 of the journey

Van
1 h -> Together minus car
-> 1/5-1/9 = 9/45-5/45 = 4/45

1 h -> 4/45 of the distance
9 h -> 4/45x9 = 4/5 of the distance
Remaining distance = 1/5 of the distance ie 1 unit left
Since van was still 180km away from Town Q -> 1 unit -> 180 km
5 units -> 5x180 km = 900 km

Distance between Town P and Town Q = 900 km

Note:
I think that there are shorter methods of solving this speed question, hope to learn from others.

[Vanilla Cake]

YLH88:

2) Greg counted the number of cars, vans and motorcycles parked at the multi-storey carpark.There were 5/9 as many vans as cars.1/4 of the number of motorcycles was 36 less than 1/5 of the number of vans.After some cars left the carpark, there was an equal number of cars and vans.Given that there was a total of 480 cars and motorcycles at the carpark at first, how many cars left the carparks ?

If I am not mistaken, this question had been posted before and already solved in KSP forum (maybe Uncle Dharma?). Cannot find the link and here's my suggested solution:

Cars
V: Vans
M: Motorcycles

Before
V : C
5u : 9u

1/4 of the number of motorcycles was 36 less than 1/5 of the number of vans-> 1/4 of M +36= 1/5 of 5u
M/4+36=u
M+144=4u
M= 4u-144

There was a total of 480 cars and motorcycles at the carpark at first,
9u+4u-144=480
13u=624
u=48

After some cars left the carpark, there was an equal number of cars and vans.
After
V : C
1p : 1p
5u : 5u

Number of cars left -> 9u-5u=4u
4u= 4x48=192
Number of cars left the carpark = 192

YLH88:

3) The capacity of a mug is 1375 ml less than the capacity of a jar.The capacity of a cup is 1/5 that of a mug.4/9 of the amount of orange cordial in a dispenser was used to fill 3 cups and 5 mugs completely.3/5 of the remaining amount of orange cordial was used to fill 2 jars completely.Find the difference between the capacity of a jar and a cup.

Mug: u-1375
Jar: u
Cup: 1/5x(u-1375)=0.2u-275

3C+5M -> 4/9 of total
2J -> 3/9 of total
2Jx9/3x4/9 -> 4/9 of total
8J/3 -> 4/9 of total

3C+5M -> 8J/3
9C+15M -> 8J

9(0.2u-275)+15(u-1375)=8u
1.8u-2475+15u-20625=8u
8.8u=23100
u=2625

Difference in capacity between a jar and a cup-> u-(0.2u-275)=u-0.2u+275=0.8u+275
0.8u+275 = 0.8(2625)+275=2100+275=2375 ml

Pls check the above calculations as I am in a sleepy mood.
Good night.
:snooze:

[Dharma]

benorito:

Dharma:

[quote=\"firebird\"]Dear maths guru


Please help me on the following maths:



2) At 9am John was cycling from Point A to Point B. At the same time, Mary was cycling from point B to point A using the same route as John. Cycliing at a speed of 4km/h faster than Mary, they would pass each other 300 meter away from the mid point.

a) What time did they pass each other?


a) Difference in distance travelled by John and Mary = 4km/h x T
T = 0.3km x 2/(4km/hr) = 3/20 hrs = 9 mins
Time they passed each other => 9.09am

Dharma,

Can you tell me why you must multiply the 0.3 km by 2 ?

Thanks

[/quote]It will be easier to imagine if Mary cycled in the same direction as John.

If T hrs was taken if the met when they were cycling in opposite direction. So, when they cycled in the same direction starting at the same time, in T hours, the distance travelled by John will be distance cycled by Mary plus 300m (up to the midpoint) and plus another 300m (after the midpoint).

# The distance cycled by John + distance cycle by Mary = Distance between Town A and Town B

If you still don’t understand, please let me know.

[YLH88]

Hi VC


Thank you so much!!

Have a nice weekend!

[Dharma]

1)At 11am, a van set off from Town P for Town Q while a car set off from Town Q for Town P.

At 4pm, the van and the car passed each other.
4 hours after they met, the car reached Town P but the van was still 180km away from Town Q.
Find the distance between Town P and Town Q.

Speed is fixed (car)
Time ratio => Q to meeting pt : Meeting pt to P = 5 : 4
Distance ratio => Q to meeting pt : Meeting pt to P = 5 : 4

Time is fixed (car & van pass each other)
Distance ratio => Van : Car = 4 : 5
Speed ratio => Van : Car = 4 : 5

5u – 4u = 180km
1u = 180km
Distance between Town P and Q = 5u = 900km

2) Greg counted the number of cars, vans and motorcycles parked at the multi-storey carpark.
There were 5/9 as many vans as cars.
1/4 of the number of motorcycles was 36 less than 1/5 of the number of vans.
After some cars left the carpark, there was an equal number of cars and vans.
Given that there was a total of 480 cars and motorcycles at the carpark at first, how many cars left the carparks ?

Vans : 5u
Cars : 9u
Motorcycles : 4(1u – 36) = 4u – 144

13u – 144 = 480
13u = 624
1u = 48
No. of cars that left the carpark = 4u = 4 x 48 = 192

3) The capacity of a mug is 1375 ml less than the capacity of a jar.
The capacity of a cup is 1/5 that of a mug.
4/9 of the amount of orange cordial in a dispenser was used to fill 3 cups and 5 mugs completely.
3/5 of the remaining amount of orange cordial was used to fill 2 jars completely.
Find the difference between the capacity of a jar and a cup.

Cup : 1u
Mug : 5u
Jar : 5u + 1375

4/9 of dispenser = 3u + 25u = 28u
3/5 x 5/9 = 1/3 of dispenser = 10u + 2750

30u + 8250 = 63u
33u = 8250
1u = 250
Difference = 4u + 1375 = 2375

[YLH88]

Hi Dharma,


Thank you so much for the solution! Have a great weekend!

Regards

[Muffins]

Hi Publica!


I have done your first problem, but first, let me tell you something. \"u\" means unit, and \"p\" means part. So, here goes:

AT FIRST - A : B
7u : 5p

AFTER FIRST TRANSFER - A : B
6u : 5p + 1u

AFTER SECOND TRANSFER - A : B
6.2u + 1p : 4p + 0.8u

6.2 u = 3p + 0.8u

Therefore, 5.4u = 3p

Dividing both by 3, we get: 1.8u = 1p

Unit : Part
5 : 9

So, first ratio: 5 X 7 : 9 X 5
35 : 45

35 : 45
= 7 : 9

[Herbie]

Hi

I have one qn
Zachery set off from the port at 6.30am and took 8 hr to reach the resort.
Robbie set off from the port 45 mins later than Zachery and took 5 hr to reach the resort. At what time did Robbie catch up with Zachery??

Many thanks!