Ali and Faizer start 27 miles apart and walk simultaneously. If they walk in…
2025
Ali and Faizer start 27 miles apart and walk simultaneously. If they walk in the same direction, with Ali catching up to Faizer, they meet after 9 hours. If instead they walk directly towards each other, they meet after 3 hours. What is Faizer's speed most likely to be?
- A.
3 mph
- B.
9 mph
- C.
6 mph
- D.
8 mph
Show answer & explanation
Correct answer: A
Concept: when two people separated by a fixed distance walk simultaneously, the gap between them closes at the SUM of their speeds if they walk towards each other (opposite directions), and at the DIFFERENCE of the faster speed minus the slower speed if they walk in the same direction with one person catching up to the other. In both cases, time taken = distance divided by that closing rate.
Let Ali's speed be X mph and Faizer's speed be Y mph; they start 27 miles apart.
Walking in the same direction with Ali catching up to Faizer, Ali must be the faster walker, so the closing rate is (X minus Y) mph and they meet after 9 hours: X minus Y = 27 divided by 9 = 3.
Walking towards each other, the closing rate is (X plus Y) mph and they meet after 3 hours: X plus Y = 27 divided by 3 = 9.
Adding the two equations: 2X = 12, so X = 6.
Substituting back: Y = 9 minus 6 = 3.
Cross-check: with X = 6 mph and Y = 3 mph, the same-direction closing rate is 6 minus 3 = 3 mph, giving time = 27 divided by 3 = 9 hours, matching the given 9 hours. The towards-each-other closing rate is 6 plus 3 = 9 mph, giving time = 27 divided by 9 = 3 hours, matching the given 3 hours. Both conditions check out, confirming Faizer's speed is 3 mph.