Yoona runs at a steady rate of 1 yard per second. Jessica runs 4 times as fast. If Jessica gives Yoona a head start of 30 yards in a race, how many yards must Jessica run to catch up to Yoona?

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40 yards

50 yards

60 yards

78 yards

answer is A.

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Detailed Solution

Yoona runs at a constant speed of 1 yard per second. Jessica runs 4 times faster than Yoona.
So Jessica's speed is 4×1=4 yards per second.
Now both are participating in the race. Jessica gives Yoona a 30 yard lead.
That means Jessica is 30 yards behind Yonna.
Suppose Jessica has to travel x yards to catch up with Yoona.
We also understand that to get a head start, Jessica started running when Yonna was already 30 yards ahead of her.
If the time taken for Jessica to cover x yards and catch up with Yoona is t seconds, then in these t seconds Jessica covers x yards while Yonna only covers (x−30) yards.
For Yoona, the value of t will be the distance traveled divided by the speed, which is
t =