Question

Mr. thomas drove his old truck to the city at a rate of 40 mi/hr and drove back home on the interstate at a rate of 60 mi/hr. the total trip took 6 hr. how far is mr. thomas home from the city

Answer 1

To solve the problem, we use the distance formula for each direction of Mr. Thomas's trip and set up an equation to solve for the distance 'd'. After calculating, we find that Mr. Thomas's home is 144 miles from the city.

Step-by-step explanation:

The student is asking for help with a mathematics problem related to distance, rate, and time. Specifically, the problem deals with finding the distance from Mr. Thomas's home to the city given the speeds at which he traveled both to the city and back, as well as the total time for the round trip.

To solve it, we can use the formula distance = rate × time for each leg of the trip and add the times together to equal 6 hours, the total time of the trip.

Step-by-Step Solution:

1. Let's denote the distance from the home to the city as 'd' miles.
2. On the way to the city, Mr. Thomas drives at 40 mi/hr, so the time taken (T1) is d/40 hours.
3. On the way back home, he drives at 60 mi/hr, thus the time taken (T2) is d/60 hours.
4. The total time taken for the trip is 6 hours, so T1 + T2 = 6.
5. Now we substitute the expressions for T1 and T2 into the equation: (d/40) + (d/60) = 6.
6. Finding a common denominator and solving for 'd' gives us the distance from Mr. Thomas's home to the city.

To find 'd', we solve the equation: d/40 + d/60 = 6. Multiplying all terms by 120 (the least common multiple of 40 and 60) to clear the denominators gives us 3d + 2d = 720. Simplifying we get 5d = 720, and dividing both sides by 5 gives us d = 144. Therefore, Mr. Thomas's home is 144 miles from the city.