Question

Kate rode her bike at 15 mi./hr to get her car. She then drove back at 45 mph. If the entire trip took her eight hours, how far away was her car?

a) 40 miles
b) 75 miles
c) 45 miles
d) 90 miles

Answer 1

Kate's car was 90 miles away. We calculated the distance by equally dividing the total travel time of 8 hours between the two speeds at which Kate traveled: 15 mph on her bike and 45 mph in her car.

Step-by-step explanation:

To solve how far away Kate's car was, we need to use the given speeds and the total time to find the distance. Kate rode her bike at a speed of 15 mph and drove back at 45 mph. Let's call the distance to her car x miles. The time it took her to ride her bike to the car is the distance x divided by the bike speed, which is x/15 hours. The time to drive back is the distance x divided by the car speed, which is x/45 hours.

The sum of these times is 8 hours (the total time for the trip), so we can write the equation:
x/15 + x/45 = 8. To solve for x, we need to find a common denominator for the fractions, which is 45:
3x + x = 360. Simplifying, we get 4x = 360, so x = 90 miles. Therefore, Kate's car was 90 miles away.