2008 AMC 10A Problem 15

Question

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?

120

130

140

150

160

Let Ian drive

t

hours at

r

miles per hour

Expanding

(r + 5)(t + 1) - rt = 70

gives

5t + r = 65

Let Ian drive

t

hours at rate

r,

covering

rt

miles.

Han drove

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

= 5t + r + 5 = 70,

so

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.

Problem 15 in other years