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
The expression for the total time of travel?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 total time of travelThe 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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