MATH SOLVE

3 months ago

Q:
# Driving to your friend's house, you travel at an average rate of 35 miles per hour. On yourhome, you travel at an average rate of 40 miles per hour. If the round trip took you 45 minuteshow far is it from your house to your friend's house?

Accepted Solution

A:

Answer:14 miles.Step-by-step explanation:Let the distance traveled from home to destination = x miles.Speed while going to friend's house = 35 miles per hour.Speed while coming back = 40 miles per hour.Total Time taken for the journey = 45 minutes = 0.75 hours.Let the time taken while going to friend's house = y hours.Therefore, the time taken while going to friend's house = (0.75 - y) hours.To find x and y, model the speeds of both the journeys.Speed while going to friend's house = Distance/Time.35 = x/y.x = 35y (Equation 1).Speed while coming back = Distance/Time.40 = x/(0.75 - y).x = 40(0.75 - y) (Equation 2).Since x = x, therefore:35y = 30 - 40y.75y = 30.y = 30/75.y = 0.4 hours.Put y = 0.4 hours in Equation 1:x = 35y.x = 35(0.4).x = 14.Therefore, the distance between my friend's house and my house is 14 miles!!!