Two friends A and B leave City P and City Q simultaneously and travel towards…
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Two friends A and B leave City P and City Q simultaneously and travel towards Q and P at constant speeds. They meet at a point in between the two cities and then proceed to their respective destinations in 54 minutes and 24 minutes respectively. How long did B take to cover the entire journey between City Q and City P?
- A.
60
- B.
36
- C.
24
- D.
48
Attempted by 24 students.
Show answer & explanation
Correct answer: A
Let the speed of the friend starting from City P be a and the speed of the friend starting from City Q be b. Let t minutes be the time until they meet.
Distance traveled by the friend from P before meeting = a·t. Distance traveled by the friend from Q before meeting = b·t.
After meeting, the friend from P takes 54 minutes to reach Q, so the remaining distance for that friend is a·54. After meeting, the friend from Q takes 24 minutes to reach P, so the remaining distance for that friend is b·24.
Because the two parts of the route meet at the same point, the distance the friend from P travels after meeting equals the distance the friend from Q traveled before meeting, and vice versa. Therefore:
b·t = a·54
a·t = b·24
Multiply the two equations:
(a·t)·(b·t) = (a·54)·(b·24) ⇒ ab·t² = ab·(54·24) ⇒ t² = 54·24
So t = √(54·24) = 36 minutes.
The friend from Q took 24 minutes after meeting plus the 36 minutes before meeting, so the total time for that friend to travel from City Q to City P is 36 + 24 = 60 minutes.
Answer: 60 minutes.