Two guys are working, each on a task of the same size, at some speed. After…
2025
Two guys are working, each on a task of the same size, at some speed. After some time, one guy realizes that he has completed only half of what the other guy has completed — and this amount is also equal to half of what is left for the other guy to complete. How much faster than the other guy must this guy now work, in order to finish at the same time as him?
- A.
3/2
- B.
2
- C.
5/2
- D.
3
Show answer & explanation
Correct answer: A
Concept: When two people must finish their remaining work at the same time, the speed each needs is proportional to how much work is still left for them, because time equals work divided by speed — so equal finishing times require the speed ratio to match the ratio of the remaining amounts of work.
Let the total work in each guy's task be W units (same-size tasks).
Guy 1 has completed half of what Guy 2 has completed: if Guy 2 has done d2, then Guy 1 has done d1 = d2/2.
This same amount d1 also equals half of what is left for Guy 2: d1 = (W - d2)/2.
Substituting d2 = 2d1 into the second equation: d1 = (W - 2d1)/2, which gives 4d1 = W, so d1 = W/4 and d2 = W/2.
Remaining work: Guy 1 has W - W/4 = 3W/4 left; Guy 2 has W - W/2 = W/2 left.
For both to finish together from here, the speed ratio must match the remaining-work ratio: Guy 1's new speed to Guy 2's current speed = 3W/4 to W/2 = 3/2.
Cross-check: taking W = 100, Guy 1 has done 25 and Guy 2 has done 50 (25 is half of 50, and it also equals half of Guy 2's remaining 50). Guy 1's remaining work is 75 and Guy 2's remaining work is 50; the ratio 75/50 = 3/2 confirms the result.
So Guy 1 must now work at 3/2 times Guy 2's current speed.