John took a drive to town at an average rate of 40mph. In te evening he drove back at 30mph. If he spent a total of 7 hours traveling, what is the distance traveled by John?
Please set up the boxes and help solve.
the answer is 240mph
explanation: 4 and 3 has a similar multiple and that is 12 meaning the question said 7 hours and he traveled 40mph to go to his destination and to go back was 30mph meaning to go to his destination it took 3 hours=120mph and to go back took 4 hours=120mph as well because to go to his destination he traveled 40mph and to go back was 30mph
To solve this problem, we can use the formula: Distance = Rate × Time.
Let's start by setting up the equation:
Let x be the distance traveled to town.
Since the rate is given in miles per hour (mph), the time taken to travel to town can be found by dividing the distance by the rate: Time = Distance/Rate = x/40.
John drove back from town at an average rate of 30 mph. The time taken to travel back can be found using the same formula: Time = Distance/Rate = x/30.
We are given that the total time taken for the entire trip is 7 hours. So, the equation becomes:
x/40 + x/30 = 7.
To solve this equation, we can find a common denominator and combine the fractions:
(3x + 4x)/(40*30) = 7,
7x/1200 = 7.
Next, we can cancel out the 7 on both sides of the equation, leaving us with:
x/1200 = 1.
Now, we can solve for x by multiplying both sides of the equation by 1200:
x = 1200.
Therefore, the distance traveled by John is 1200 miles.
Here's the visual setup:
Distance to town: x
Rate to town: 40 mph
Time to town: x/40
Distance back from town: x
Rate back from town: 30 mph
Time back from town: x/30
Total time: 7 hours
Equation: x/40 + x/30 = 7
Let x be the hours driving out.
So, the distance out is 40*x, which must be equal to the distance back 30*(7-x)
40*x = 30*(7-x). Solve for x, and the rest will fall in place.