Mike drove to a friends house at a rate of 40 mph he returned by the same route at 45 mph The driving time round trip was 4 hours. write and solve an equation to find the distance Mike traveled
since time = distance/speed,
d/40 + d/45 = 4
d = 84.7 miles
round trip = 169.4 miles
check:
84.7/40 = 2.118
84.7/45 = 1.882
total: 4.000 hours
To find the distance Mike traveled, we need to set up an equation based on the given information. Let's first define some variables:
Let the distance Mike traveled be represented by "d".
The equation for calculating time is:
Time = Distance / Speed
According to the problem statement:
For the outbound journey:
distance = d
speed = 40 mph
time = d / 40
For the return journey:
distance = d
speed = 45 mph
time = d / 45
The total time for the round trip is given as 4 hours. Therefore, the equation is:
(d / 40) + (d / 45) = 4
To solve this equation, we can first find the common denominator of 40 and 45, which is 360. Multiplying each term by 360, we get:
9d + 8d = 4 * 360
17d = 1440
Dividing both sides of the equation by 17, we find:
d = 1440 / 17
Using a calculator, we can find that d ≈ 84.71 miles (rounded to two decimal places). Therefore, Mike traveled approximately 84.71 miles.