Operations & Word Problems

Problem

Distance grows in proportion to time

A car goes 18 mi 900 yd in 15 minutes at a steady speed. We must find how far it goes in 25 minutes. We convert the distance to a single unit (yards), find the distance per minute, multiply by 25, then convert back to miles and yards.
Measurement & dataOperations
Your answer
How to solve
Strategy Analyze the Units — Constant speed means distance per minute is fixed, so the natural plan is: convert the distance to yards, find yards-per-minute, multiply by the new time, then regroup back into miles and yards. Splitting it into these unit-driven subproblems keeps the arithmetic simple for an elementary learner.
1STEP 1

Convert the 15-minute distance to yards

Since 1 mi = 1760 yd, 18 mi = 31680 yd; adding the extra 900 yd gives 32580 yd in total.

18 × 1760 + 900 = 31680 + 900 = 32580 \text{ yd}
2STEP 2

Find the distance per minute

The car covers 32580 yd in 15 minutes at a steady speed, which works out to 2172 yd every minute.

32580 ÷ 15 = 2172 \text{ yd per minute}
3STEP 3

Multiply by 25 minutes

For 25 minutes, multiply the per-minute distance by 25.

2172 × 25 = 54300 \text{ yd}
4STEP 4

Convert back to miles and yards

Regroup 54300 yd into whole miles plus leftover yards: that's 30 mi 1500 yd.

54300 ÷ 1760 = 30 \text{ mi remainder } 1500 \text{ yd}
Answer
30 mi 1500 yd
54300 yd ÷ 1760 = 30 mi remainder 1500 yd → 30 mi 1500 yd
25 minutes is more than 15 minutes, so the distance should be larger than 18 mi 900 yd — and 30 mi 1500 yd is indeed larger. As a rough check, 25/15 is about 1.67, and 18 mi times 1.67 is about 30 mi, matching our result.
Takeaway

At a steady speed, find how far you go in one minute, then multiply by the new minutes — same speed, more time, more distance!

  • Convert the 15-minute distance to yards
  • Find the distance per minute
  • Multiply by 25 minutes
  • Convert back to miles and yards
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