2008 AMC 10A Problem 15

Problem 15 of 25IntermediateAlgebra Arithmetic

Yesterday Han drove

1

hour longer than Ian at an average speed

5

miles per hour faster than Ian. Jan drove

2

hours longer than Ian at an average speed

10

miles per hour faster than Ian. Han drove

70

miles more than Ian. How many more miles did Jan drive than Ian?

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Solution

Let Ian drive

t

hours at rate

r,

covering

rt

miles. Han drove

(r + 5)(t + 1) - rt

= 5t + r + 5 = 70,

5t + r = 65.

Jan drove

(r + 10)(t + 2) - rt

= 10t + 2r + 20

= 2(5t + r) + 20

= 2 \cdot 65 + 20

= 150

miles more than Ian. Thus, the correct answer is D.

Tagged: distance rate and time · system of equations · algebraic manipulation