MathDB
Reverse Roads

Source: 2017 AMC 10A #9

February 8, 2017
AMCAMC 10AMC 10 A2017 AMC 10A

Problem Statement

Minnie rides on a flat road at 2020 kilometers per hour (kph), downhill at 3030 kph, and uphill at 55 kph. Penny rides on a flat road at 3030 kph, downhill at 4040 kph, and uphill at 1010 kph. Minnie goes from town AA to town BB, a distance of 1010 km all uphill, then from town BB to town CC, a distance of 1515 km all downhill, and then back to town AA, a distance of 2020 km on the flat. Penny goes the other way around using the same route. How many more minutes does it take Minnie to complete the 4545-km ride than it takes Penny?
<spanclass=latexbold>(A)</span> 45<spanclass=latexbold>(B)</span> 60<spanclass=latexbold>(C)</span> 65<spanclass=latexbold>(D)</span> 90<spanclass=latexbold>(E)</span> 95<span class='latex-bold'>(A)</span>\ 45\qquad<span class='latex-bold'>(B)</span>\ 60\qquad<span class='latex-bold'>(C)</span>\ 65\qquad<span class='latex-bold'>(D)</span>\ 90\qquad<span class='latex-bold'>(E)</span>\ 95