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.
Gretchen will pick up the baton in 12 seconds.
The distance covered by Mika in 12 seconds is
Therefore, Mika will be 36 meters away from the current location.
If the two angles are a linear pair, this means that they are supplementary and both add up to 180 degrees. So set up the equation:
3x + 7 + 9x + 17 = 180
--> 3x + 9x + 17 + 7 = 180
--> 12x + 24 = 180
-->12x = 180 - 24 = 156
-->156/12 = 13, so x = 13
Plug in the x value:
3(13) + 7 = 46 degrees
9(13) + 17 = 134 degrees
To check your work, 134 + 46 = 180.
Your answer is A.
3(13) + 7 = 46
9(13) + 17 = 134
Which concludes that your answer is A!