Question

Gabriella drives her car 400 miles and averages a certain speed. If the average speed had been 7 mph less she could have traveled only 350 miles in the same length of time what is her average speed

Answer 1

Gabriella's average original speed was 56
`(mi)/(h)`

Explanation:

Let's use the equation that defines the average speed "v" of Gabriella during the time (t) that her trip took:

`v = (distance)/(time) \\v=(400)/(t)`

Next let's write a similar average speed equation for the case in which she drove at (v - 7 mi/h) during the same time "t" and covered 350 miles:

`(v-7)=(350)/(t)`

Notice that the time "t" in the denominator appears equally in both equations we wrote, so let's isolate them on the right:

`(v)/(400) =(1)/(t) \\and\\((v-7))/(350) =(1)/(t)`

now equal both expression since they both share the same value on the right, and solve for the unknown "v":

`(v)/(400) =((v-7))/(350) \\350\,v=400\,(v-7)=\\350\,v=400\,v-2800\\2800=50\,v\\v=(2800)/(50) \,\,(mi)/(h)\\v=56\,\,(mi)/(h)`