Larry travels 60 miles per hour going to a friend's house and 50 miles per hour coming back, using the same road. He drives a total of 5 hours. What is the distance from Larry's house to his friend's house, rounded to the nearest mile?
(A) 110
(B) 126
(C) 136
(D) 154
Answer (2)
Define the distance as d , and times as t 1 and t 2 .
Express times in terms of distance: t 1 = 60 d and t 2 = 50 d .
Substitute into the total time equation: 60 d + 50 d = 5 .
Solve for d : d = 11 1500 ≈ 136 miles. The final answer is 136 .
Explanation
Problem Analysis Let's analyze the problem. Larry travels to his friend's house at 60 mph and returns at 50 mph. The total travel time is 5 hours. We need to find the distance to his friend's house.
Define Variables Let d be the distance from Larry's house to his friend's house. Let t 1 be the time it takes Larry to travel to his friend's house, and t 2 be the time it takes Larry to return home.
Formulate Equations We know that distance = speed × time. Therefore, we have the following equations:
d = 60 t 1 (going to the friend's house)
d = 50 t 2 (returning home)
t 1 + t 2 = 5 (total travel time)
Express Time in Terms of Distance From the first two equations, we can express t 1 and t 2 in terms of d :
t 1 = 60 d
t 2 = 50 d
Substitute into Total Time Equation Substitute these expressions for t 1 and t 2 into the third equation:
60 d + 50 d = 5
Solve for Distance To solve for d , we first find a common denominator for the fractions, which is 300. Multiply both sides of the equation by 300:
300 ( 60 d + 50 d ) = 300 ( 5 )
5 d + 6 d = 1500
11 d = 1500
Calculate Distance Now, divide both sides by 11 to find the distance d :
d = 11 1500 ≈ 136.36
Round to Nearest Mile Since we need to round the distance to the nearest mile, we have:
d ≈ 136 miles
Final Answer Therefore, the distance from Larry's house to his friend's house is approximately 136 miles.
Examples
Understanding distance, speed, and time relationships is crucial in everyday life. For instance, if you're planning a road trip, knowing the distance to your destination and the speed you'll be traveling helps you estimate the travel time. Similarly, delivery services use these calculations to optimize routes and provide accurate delivery estimates. This problem demonstrates how these concepts are applied to solve practical problems involving travel.
The distance from Larry's house to his friend's house is approximately 136 miles, calculated by solving the total travel time equation based on his speeds to and from the destination. The correct answer option is (C) 136.
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