it took us 3 hour to drive to a concert.on his way home he increased his speed by 19 miles got home in 2 hours . what was the speed

first speed --- x mph

2nd speed --- x+19 mph

d/x = 3 ---> d = 3x
d/(x+19) = 2 --- d = 2x + 38

3x = 2x+38
x = 38

first speed = 38 mph
2nd speed = 57 mph

check:
distance = 3(38) = 114
or 2(57) = 114

time for 1st trip = 114/38 = 3 hrs
tiem for 2nd trip = 114/57 = 2 hrs

hank you Reiny.

To find the speed, we need to know the distance traveled. The distance can be calculated by multiplying the time taken by the speed.

Let's start by finding the distance traveled on the way to the concert. We know that it took 3 hours to drive there, but we don't have the speed. Let's call it "x" for now.

Distance to the concert = Speed x Time
Distance = x * 3

On the way back home, the speed increased by 19 miles per hour, and it took 2 hours to get home. So we can calculate the distance using the same formula.

Distance back home = (Speed + 19) x 2
Distance = (x + 19) * 2

Since the distance traveled to the concert and back home is the same, we can set these two equations equal to each other:

x * 3 = (x + 19) * 2

Let's solve this equation to find the value of x, which represents the initial speed.

3x = 2(x + 19)
3x = 2x + 38
x = 38

Therefore, the initial speed on the way to the concert was 38 miles per hour.