Track / Stage 5 / 121 of 400 #721 of 2000

Problem 721

AIME late

Algebra Difficulty 5.3 Find the answer

A4. Marija travels to school by a combination of walking and skateboarding. She can get there in 38 minutes if she walks for 25 minutes and skateboards for 13 , or in 31 minutes if she walks for 11 and skateboards for 20 . How long (in minutes) would it take her to walk to school?

Your answer

Official solution

Solution 1: Denoting her walking speed by $w$ , skateboarding speed by $s$ , and distance to school by $D$ , we have
$D=25 w+13 s, \quad \text { and } D=11 w+20 s .$

Subtracting these gives $7 s=14 w$ , and so $D=51 w$ . Hence, it will take 51 minutes.
Solution 2: Decreasing the skateboarding time by 7 minutes increases the walking time by $14=2 \times 7$ minutes and the total time taken by 7 minutes. So decreasing the skateboarding time by 13 minutes will increase the walking time by $26=2 \times 13$ minutes and the total time by 13 minutes, from 38 to 51 .
Answer: 51 .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.