Carcass wrote:
A and B can run one full round of a circular track in 8 minutes and 15 minutes respectively. If they start simultaneously and run in same direction, after how much time will they meet for the first time?
A. 24 mins
B. 120/7 mins
C. 120/17 mins
D. 120/23 mins
E. 120 mins
In other words, the question is asking us
how long it will take A to lap B for the first time.
Since
laps the only unit of measurement, let's convert each person's speed to laps per minute.
If A can run 1 lap in 8 minutes, then A's rate is
1/8 laps per minute.
If B can run 1 lap in 15 minutes, then B rate is
1/15 laps per minute.
When A laps B for the first time, A will have traveled 1 lap further than B has, so let's start with the following word equation:
(number of laps traveled by A) = (number of laps traveled by B) + 1Distance = (rate)(t).
If we let t = the travel time for each runner, we can plug our values into the word equation to get:
(1/8)(t) = (1/15)(t)) + 1Eliminate the fractions by multiplying both sides of the equation by 120 (the LCM of 8 and 15) to get:
15t= 8t + 120This becomes:
7t= 120And then:
t= 120/7 (minutes)
Answer: B