There was terrible traffic on the highway, and Kiran drove to work at 15 miles per hour. How fast would he need to drive home for the average speed for his round trip to be 25 miles per hour
Let's assume Kiran has to travel a distance of D miles to work.
Since Kiran drove to work at 15 mph, the time it took for him to drive to work is D/15 hours.
For the round trip, Kiran will travel a total distance of 2D miles.
The total time for the round trip is (D/15) + (D/x), where x is the speed at which Kiran drives home.
Since we know the average speed for the round trip needs to be 25 mph, the total time should be (2D)/25 hours.
Setting up the equation, we have:
(D/15) + (D/x) = (2D)/25.
Now we can solve for x:
Multiply through by 75 to clear the denominators:
5D + 75(D/x) = 6D.
Simplifying, we have:
5Dx + 75D = 6Dx.
Rearranging, we get:
Dx = 75D.
Dividing both sides by D, we find:
x = 75.
Therefore, Kiran would need to drive home at a speed of 75 mph for the average speed for his round trip to be 25 mph.