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Help needed on Distance/Rate question

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by madsport » Mon Aug 25, 2008 9:15 am
The time it took car A to travel 400 miles was 2 hours less the time it took car B to travel the same distance. If car A's average speed was 10 miles per hour greater than that of car B, what was car B's average speed, in miles per hour?

A) 20
B) 30
C) 40
D) 50
E) 80

The answer is C. Along with the solution steps, feel free to add any full proof strategies on solving similar problems. This is big hurdle for me.

Thanks in advances, ladies and gents!! :-)
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by pepeprepa » Mon Aug 25, 2008 9:31 am
Let's write the information.

t=d/v
t is the time of B
v is the speed of B

A
t-2=400/(v+10)
B
t=400/v

You can join both
400/(v+10) +2 = 400/v

And you solve v given you have 1 unknown and 1 equation
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by anju » Mon Aug 25, 2008 12:55 pm
I used backsolving method.. answers are provided.
A B
R x+10 x
T t-2 t
D 400 400

Start with C: if x=40, t = 10
x+10 = 50 and t-2 = 8
now RT of A = RT of B since distance is same
so 50*8 = 40*10
400 = 400 so choice C is correct
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