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?

$120$

$130$

$140$

$150$

$160$

Answer: D

Concepts:distance rate and time system of equations algebraic manipulation

Difficulty rating: 1440

Solution:

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.

2008 AMC 10A Problem 15

Answer: D

Difficulty rating: 1440

Solution:

Problem 15 in Other Years