Question

Question 6 of 15, Step 1 of 1

Correct
Jessie recently drove to visit her parents who live 385 miles away. On her way there her average speed was 24 miles per hour faster than on her way home (she ran into
some bad weather). If Jessie spent a total of 11 hours driving, find the two rates (in mph). Round your answer to two decimal places, if needed.

Answer 1

Answer: 84 mph 60 mph

Explanation:

Let her average speed to home was x mph

Hence, the average speed to her parents was (x+24) mph

Thus:

Jessie spent for the trip to her parents' house: 385/x hours

Jessie spent for the trip to home: 385/(x+24) hours

`\displaystyle\\(385)/(x) +(385)/(x+24) =11\\\\385(x+24)+385(x)=11(x)(x+24)\\\\385x+9240+385x=11x^2+264x\\\\770x+9240=11x^2+264x\\\\770x+9240-770x=11x^2+264x-770x\\\\9240=11x^2-506x\\\\9240-9240=11x^2-506x-9240\\\\0=11x^2-506x-9240\\\\Divide\ both\ parts\ of\ the \ equation\ by\ 11:\\\\0=x^2-46x-840`

`\displaystyle.\\Thus,\\\\x^2-46x-840=0\\\\D=(-46)^2-4*1*(-840)\\\\D=2116+3360\\\\D=5476\\\\√(D) =√(5476) \\\\√(D)=74 \\\\x=(466б74)/(2*1) \\\\x=(46-74)/(2) \\\\=(-28)/(2) \\\\x=-14\\otin(x > 0)\\\\x=(46+74)/(2)\\\\x=(120)/(2) \\\\x=60\ miles\ per\ hour`

`60+24=84\ miles\ her\ hour`