Question

Gretchen and Mika are involved in a relay race. Both runners are at the same point on the course when Gretchen realizes that she dropped her baton and has to turn around to retrieve it. Gretchen runs backwards at a speed of −4 m/s, relative to the direction of the race. Mika continues running at a speed of 3 m/s. If Gretchen dropped her baton −48 meters from her current location, relative to the direction of the race, how far ahead will Mika be when Gretchen picks her baton up?
________ meters

Answer 1

Solution: Mika will be 36 meters away from the current location.

Explanation:

It is given that Gretchen and Mika are at the same point when Gretchen runs backward at the speed of 4 m/s in opposite direction to pick her baton and Mika runs in the direction of the race at the speed of 3 m/s.

We have find the distance covered by Mika form the current location in the time when Gretchen picks her baton up.

Let the time taken by Gretchen picks her baton up be t.

It is given that 48 meters from her current location she dropped her baton. Since she is running at the speed of 4 m/s.

$t=\frac{48}{4} =12$

Gretchen will pick up the baton in 12 seconds.

The distance covered by Mika in 12 seconds is $3\times 12=36$

Therefore, Mika will be 36 meters away from the current location.

Answer 2

The baton is dropped -48m from the current position, and Gretchen runs backwards at a speed of -4m/s, so it will take her -48m/(-4m/s) or 12 seconds before she picks up her baton.

During these 12 seconds, Mika will have traveled 3m/s*12s=36m.