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?

84 meters

Step-by-step explanation:

They are in the same point, let's call the point x.

They were originally at point x.

Baton was at -48 meters

If Gretchen ran back at -4 m/s

It took her -48/-4 or 12 seconds

During that 12 seconds, Mika ran forward 3 meters per second, or 3*12 = 36 meters total.

Gretchen is 48 meters behind point x, while Mika is 36 meters ahead.

You add the two amounts up to get: 36 + 48 = 84.

This means that Mika will be 84 meters ahead of Gretchen.

Let me know if you have any questions, hope this helped!

shift 4 units up, and 1 unit left.

it will translate f(x) = 3^x to g(x) = 3^(x+1) + 4