One car went 10 miles farther when traveling at 50 mph than a second car that traveled 2 hours longer at a speed of 40 mph. How long did the first car travel?
times t hours and (t+2) hours)
d1 = 50 t
d2 = 40(t+2)
50 t = 10 + 40(t+2)
10 t = 90
t = 9
To find out how long the first car traveled, we can start by setting up equations for both cars.
Let's say the time traveled by the second car is represented by t hours. Therefore, the time traveled by the first car would be t + 2 hours.
Now, let's convert the given information into equations:
First car's speed = 50 mph
First car's time = t + 2 hours
Second car's speed = 40 mph
Second car's time = t hours
Distance Traveled = Speed x Time
Using this formula, we can set up the equations:
Distance traveled by the first car = Distance traveled by the second car + 10 miles
50(t + 2) = 40t + 10
Now, let's solve this equation to find the value of t, which will give us the time traveled by the first car:
50t + 100 = 40t + 10
50t - 40t = 10 - 100
10t = -90
Dividing both sides by 10:
t = -9
We have found that t = -9. However, this is not a valid solution since time cannot be negative. Therefore, the first car did not travel for a negative amount of time.
Hence, in this particular scenario, there is no valid solution for how long the first car traveled.