Amy drove on the highways at 70 miles/hour to pick up fruits from her grandma’s garden in the morning. She stayed there for two hours. When coming back in the afternoon, she drove on the local roads at 40 miles per hour to avoid traffic. She spent a total of 8 hours for this trip, and drove a total 300 miles. How many miles did she drive each way?

Here is my diagram of Amy's trip. She drove from her home H to grandma's house H on a direct fast route. In the afternoon she drove home on local roads, a more indirect route.

diagram

Suppose the distance she travelled to grandma's house was d1 miles and it took her t1 hours, and the distance she travelled from grandma's house to home was d2 miles and it took her t2 hours.

What facts do you know? The total distance she travelled was 300 miles so

d1+d2=300 miles.

She spent t1+t2 hours driving and 2 hours at grandma's house and her total time was 8 hours. Thus

t1+t2+2=8 hours.

On the trip to grandma's house she drove d1 miles in t1 hours and her speed was 70 miles per hour so

70=d1t1 or 70×t1=d1.

Likewise for the return trip we get

40×t2=d2.

I would suggest that you solve the first equation for d1 and the second equation for t1 and substitute these values into the third equation. This converts the third equation to one involving d2 and t2. The fourth equation also involves d2 and t2. Solve these two equations for d2 and t2.

Penny

Step-by-step explanation:

step-by-step explanation:

try remembering the steps

351°f

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