Track / Stage 5 / 129 of 400 #729 of 1964

Problem 729

AIME late

Algebra Difficulty 5.2 Find the answer

A cyclist traveled 96 km 2 hours faster than he had planned. During this time, for each hour, he traveled 1 km more than he had planned to travel in 1 hour and 15 minutes. At what speed did he travel?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Solution.

Let $V$ be the speed at which the cyclist was traveling, $\frac{1 \cdot V-1}{1 \frac{15}{60}}$ - the speed at which the cyclist intended to travel. According to the condition $\frac{96}{V}+2=\frac{96}{\frac{V-1}{1 \frac{1}{4}}}$ , from which $V=16$ (km/h).

Answer: 16 km/h.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.