Question

Jessie recently drove to visit her parents who live 525 miles away. On her way there her average was 24 miles per hour faster than on her way home (she ran into bad weather). If Jessie spent a total of 15 hours driving, find the two rates.

Jessies average spend to her parents house_____mph
Jessies average spend from her parents house____mph

Answer 1

Jessie's average spend to her parent's house 84 mph.

Jessie's average spend from her parent's house 60 mph.

Explanation:

Let, Jessie's average spend to her parent's house is x mph and Jessie's average spend from her parent's house is y mph.

Now, given that, x = y + 24 ............... (1)

And,
`(525)/(x) + (525)/(y) = 15`

⇒ 35x + 35y = xy ................ (2)

Now, solving equations (1) and (2) we get,

35(y + 24) + 35y = (y + 24)y

⇒ 70y + 840 = y² + 24y

⇒ y² - 46y - 840 = 0

⇒ y² - 60y + 14y - 840 = 0

⇒ (y - 60)(y + 14) = 0

⇒ y = 60 mph {As y can not be negative}

So, x = y + 24 = 84 mph

Therefore, Jessies average spend to her parents house 84 mph.

Jessies average spend from her parents house 60 mph. (Answer)