Race Problem - Need Help

[pesfunk]

Please provide EXPLANATIONS with your answer.

A and B ran, at their respective constant rates, a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B's speed in m/s?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20

OA LATER

[limestone]

Hi,

In the first scenario, A finished less than B 1/10th of a minute or 6 seconds. And A gives B a head start of 48m ( If I do not misunderstand : A would start after B had run 48m).
In the second scenario, A finished more than B 1/30th of a minute or 2 seconds. And A gives B a head start of 144m.

As the time for A to finish the distance of 480 for the two scenarios is unchanged.
The distance left B need to move in the first scenario when A start : 480 - 48 = 432
The distance left B need to move in the first scenario when A start : 480 - 144= 336
Discrepancy in distances B moved of the two cases : 432 - 336 = 96
Discrepancy in times : 6 + 2 = 8. As in 1st case, A is less than B 6 seconds, -- in 2nd case, A is more than B 2 seconds.
Thus between the two cases, B time's discrepancy is 8 seconds.

Speed of B is : 96 / 8 = 12m/s

So pick A.

[pesfunk]

I didnt understand the discrepancy part

Hi,

In the first scenario, A finished less than B 1/10th of a minute or 6 seconds. And A gives B a head start of 48m ( If I do not misunderstand : A would start after B had run 48m).
In the second scenario, A finished more than B 1/30th of a minute or 2 seconds. And A gives B a head start of 144m.

As the time for A to finish the distance of 480 for the two scenarios is unchanged.
The distance left B need to move in the first scenario when A start : 480 - 48 = 432
The distance left B need to move in the first scenario when A start : 480 - 144= 336
Discrepancy in distances B moved of the two cases : 432 - 336 = 96
Discrepancy in times : 6 + 2 = 8. As in 1st case, A is less than B 6 seconds, -- in 2nd case, A is more than B 2 seconds.
Thus between the two cases, B time's discrepancy is 8 seconds.

Speed of B is : 96 / 8 = 12m/s

So pick A.

[limestone]

Let's take the point of time when A started to be the initial point of time. The time for A to move 480m is X

From that point of time:

In 1st case: B had moved 480 - 48 = 432m in a period of time : X + 6 ( A beats B 1/10 minutes, or time of B is 6 seconds more than that of A)
In 2nd case: B had move 480 - 144 = 336m in a period of time : X- 2 ( A is beaten 1/30 minutes, or time of B is 2 seconds less than that of A)

Now, we have:

B moved 432m in (X+6) seconds
B moved 336m in (X-2) seconds.
Then it took B more (X+6) - (X-2) seconds to move more (432 - 336)m
Or it took B more 8 seconds to move more 96m
So the speed of B must be: 96/8 = 12m/second

Hope it helps.

[hdk2104]

Alternative Approach here:

A starts from the start line and runs till the finish line in both the races. He would take the same time in both the cases then. On the other hand, in the first race, B takes 6 secs more than A while in the second race, B takes 2 secs less than A.
So there is a time difference of 8 secs in the time taken by B in the two cases. B travels (144 - 48 =) 96 m less in the second race and taken 8 secs less in the second race. This means that in the first race, B runs a distance of 96m in 8 secs.
So speed of B = 96/8 = 12 m/sec