Tutor MathsGuru: Ask me for your burning Maths questions!

[elkniwt]

Hi,


I got a different ans.

When Sam and Ruth met, Sam has travelled 3 parts and Ruth 5 parts.


|----Sam----X--------Ruth-----------|
|----|----|----|----|----|----|----|----|
When Sam and Ruth met (point X) , Sam has travelled 3 parts and Ruth 5 parts.

Between midpt and the place they met is 1 unit.
1 u = 30
8 u = 30 x 8 = 240 km
Distance between A & B = 240 km
Sam's speed = 240 / 5= 48 km/h

Dharma:

When Sam and Ruth met each other, they both travelled the same time (so, time is fixed)

Speed ratio => Sam : Ruth = 3 : 5
Distance ratio => Sam : Ruth = 3 : 5
5u – 3u = 2u = 30
1u = 15
Distance between Town A and B = 8u = 8 x 15km = 120km

Sam’s average speed = 120km/ 5hrs = 24km/hr

[elkniwt]

Herbie:

I have another speed qn.


Rose and Stella travelled from Town A to Town B along the same road but at different speeds.
Rose started her journey 45 min earlier than Stella but Stella reached Town B 20 minutes earlier.

When Stella reached Town B, Rose had travelled 7/8 of the journey and was 25 km away from Town B.
If Rose and Stella travelled at a constant speed.

a. What is the distance btw TOwn A and B? is the ans 175km?
b. What speed was Rose travelling at?
c. How long did Stella take to travel from Town A to Town B.


Tx

Hi Herbie,

Let me try ..
a)When Stella reached Town B, Rose had travelled 7/8 of the journey and was 25 km away from Town B. This means that 1/8 of the distance between A & B = 25 km
Distance btw A & B = 25 x 8 = 200 km

b) Rose's speed = 25km / 20 mins = 75 km/h (because Rose took 20 mins to complete the 25km)

c) Time taken by Stella = 7 * 20 - 45 = 95 mins (because Rose started 45 mins earlier)

Regards.

[Herbie]

Hi Dharma,


Sorry, i need to seek clarification.

Based on the question, if we fixed the time ratio as fixed

Shld the solution be written in the following way:

Time ratio => Sam : Ruth = 5 : 3
Speed ratio => Sam : Ruth = 5 : 3

Does Speed ratio = Distance ratio?

Hence Distance ratio => Sam : Ruth = 3 : 5

Please advise.

Many thanks!

[Dharma]

Herbie:

Hi Dharma,


Sorry, i need to seek clarification.

Based on the question, if we fixed the time ratio as fixed

Shld the solution be written in the following way:

Time ratio => Sam : Ruth = 5 : 3
Speed ratio => Sam : Ruth = 5 : 3

Does Speed ratio = Distance ratio?

Hence Distance ratio => Sam : Ruth = 3 : 5

Please advise.

Many thanks!

Hi Herbie,

Firstly, we need to know the speed ratio of Sam and Ruth. We know that the time taken by Sam and Ruth is 5hrs and 3 hrs respectively from one town to the other.

Here the distance between the 2 towns is fixed.
Speed ratio => Sam : Ruth = 3 : 5 (Inverse of time ratio)

Speed is fixed throughout. So, now we know that Sam and Ruth will move towards each other until they reach the meeting point.

When they meet, time is constant…. Speed ratio is proportional to distance ratio
Distance ratio => Sam : Ruth = 3 : 5

(5u – 3u)/2 = 30km [Sorry … was careless earlier]
1u = 30km

Distance between the 2 towns = 8u = 240km

Speed of Sam = 240km/5hrs = 48km/hr

# You ratios in bold is incorrect. Time and speed is ALWAYS inversely proportional to each other.
Speed ratio = Distance ratio provided time is constant.

[Herbie]

Hi Dharma,


I dun understand why (5u – 3u)/2 I tot is 5u-3u = 2u hence 2u=30km

[Dharma]

Herbie:

Hi Dharma,


I dun understand why (5u – 3u)/2 I tot is 5u-3u = 2u hence 2u=30km

Hi Herbie,

When they met, Sam travelled 3u while Ruth travelled 5u. Distance between the 2 towns is 8u.
So, midpoint is 4u from either town. So, difference in distance from the meeting point to midpoint is (4u – 3u) = 1u or (5u – 3u)/2 = 1u

(5u – 3u) = 2u = 30 is incorrect because 2u is the difference in distance travelled by Sam and Ruth and it is not 30km.

30km is half of the difference in distance travelled by Sam and Ruth (it is the distance from meeting point and midpoint)

Sam travelled 1u less than distance from Town A to mid-point and Ruth travelled 1u more than the distance from Town B to midpoint.

[Dharma]

tiger262:

Can anyone post a solution for this speed question?


Kumar and Clara started jogging along a circular track.
Kumar started at Point M while Clara started at Point N where the line MN formed the diameter of the circle.
Kumar and Clara jogged toward each other along the circular track from their respective starting point and first met at Point P which was 80 m from Point M.
After they met for the first time, they continued jogging along the track and finally met again for the second time at Point Q which was 60 m from Point N. Find the distance of the circular track.

Thank you so much.

When Kumar met Clara for the 1st time at P ; he had jogged for 80m from M.
When Kumar met Clara for the 2nd time at Q; he would have jogged another 160m (2 x 80m) from P.

So, distance from P ->N -> Q = 160m
Distance PN = 160m – 60m = 100m
Circumference of the jogging track = 2 x (80m + 100m) = 360m

[Almighty]

Dharma:

Almighty:

[quote=\"Almighty\"]

[/quote]
Thanks Dharma.There must be a printing mistake in the book...

[Almighty]

Dharma:

Herbie:

Hi Herbie,

The question is telling us when Sam and Ruth meet, they are 30km away from the mid-point of Town A and Town B

You have considered distance as fixed (From Town and Town B) and you found the time and speed ratios but you cannot mix speed/time with distance in an addition/subtraction equation.

The 30km given is DISTANCE ….you cannot subtract time /speed between Sam and Ruth and equate it to distance.

You need to understand what the qn is asking us and apply the appropriate ratio to solve the question.

The question is about meeting of 2 persons. For meeting questions; we know time taken is the same IF both departed at the same time. (Time is constant)

We know the time ratio …. But we need to find the distance ratio. REASON : Qn gives us the difference in distance travelled by Sam and Ruth. (i.e. 30km)

Even my teacher never explains like you Dharma. Thankyou very much Dharma. Thankyou Herbie for posting such questions.

[Dharma]

Herbie:

I have another speed qn.

Rose and Stella travelled from Town A to Town B along the same road but at different speeds.
Rose started her journey 45 min earlier than Stella but Stella reached Town B 20 minutes earlier.

When Stella reached Town B, Rose had travelled 7/8 of the journey and was 25 km away from Town B.
If Rose and Stella travelled at a constant speed.

a. What is the distance btw TOwn A and B? is the ans 175km?
b. What speed was Rose travelling at?
c. How long did Stella take to travel from Town A to Town B.


Tx

a)\t1/8 of the journey => 25km
8/8 of the journey => 25km x 8 = 200km (Distance between Town A and B)

b)\tRose will cover the last 25km of her journey in 20 mins
20 mins => 25km
60 mins => 75km
Rose’s speed = 75km/h

c)\tTime taken by Rose => 20 x 8 = 160 mins
Rose started 45 mins earlier and ended 20 mins later. Therefore, Stella took 65 mins lesser than Rose to complete her journey.
Time taken by Stella = 160 mins – 65 mins = 95 mins