The Escobar family went on a car trip. They drove 100 miles on country roads and 240 miles on the highway. They drove 50% faster on the highway than on the country roads. Let r represent their rate on country roads in miles per hour. a. Write and simplify an expression that represents the number of hours it took the Escobar family to complete their trip in terms of r. (Hint: 50% faster means 150% of the original rate.) b. Find their total travel time if they drove the posted speed limit.

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Explanation:

The expression that represents the number of hours it took the Escobar family to complete their trip in terms of r is 260/r

Let r represent their rate on country road and R represent their rate on highway.

So, we have:

R = (100% + 50%) * r

Evaluate

R = 1.5r

Rate is calculated using:

Rate = Distance/Time

So, we have:

r = 100/t and R = 240/T

Make T and t the subject

t = 100/r and T = 240/R

The total time of travel is:

Total = t + T

So, we have:

Total = 100/r + 240/R

Substitute R = 1.5r

Total = 100/r + 240/1.5r

Simplify

Total = 100/r + 160/r

Evaluate the sum

Total = 260/r

The speed limit is 40mph

This means that:

r = 40

In (a), we have:

Total = 260/r

Substitute 40 for r

Total = 260/40

Evaluate

Total = 6.5

Hence, their total time of travel is 6.5hours

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