Question

20. Amy drove to a friend's house at a rate of 45 mph. She returned by the same route at a rateof 50 mph. The driving time for the round trip was 4 hours. What is the total distance Amytraveled?

Answer 1

Let x represent the distance on her way to her friend's house and also the distance travelled on returning

Time = distance/speed

The rate or speed at which Amy dove to her friend's house is 45mph

Time spent in travelling to her friend's house is x/45

The rate or speed at which Amy returned from her friend's house is 50mph

Time spent in travelling returning from her friend's house is x/50

The time for the round trip is the total time spent in going and returning. This means that

`\begin{gathered} (x)/(45)\text{ + }\frac{x}{50\text{ }}\text{ = 4} \\ \text{Multiplying both sides of the equation by 2250, it becomes} \\ 50x\text{ + 45x = 9000} \\ 95x\text{ = 9000} \\ x\text{ = }(9000)/(95) \\ x\text{ = 95} \\ \text{The total distance is } \\ 95\text{ }*2\text{ = 190 miles} \end{gathered}`