Question

Quinn went to the coffee shop traveling 9mph and returned home traveling 15mph. The total trip took I hours. How long did Quinn travel at each speed?

Answer 1

to the shop : 5/8 of an hour

back home : 3/8 of an hour

Explanation:

We use the relationship between distance travelled, speed and time given by the formula:

speed = distance / time

We know that the distance from home to the coffee shop is D (same for trip back)

We also know the two speeds in one direction 9 mph and in the other 15 mph

then we can find the times t1 (to the coffee shop) and back (t2) by using the equations:

D = 9 * t1

D = 15 * t2

1 = t1 + t2

We set the two distances equal to have:

9 * t1 = 15 * t2

then t1 = 15 * t2 / 9 = 5 t2 / 3

and use this to substitute for t1 in the last equation:

t1 + t2 = 5 t2/3 + t2 = 1

8 t2 /3 = 1

then t2 = 3/8 of an hour

and therefore t1 must be 1 - t2 = 5/8 of an hour