A car and a bus leave at the same time from same location. The speed of the car is 7mph faster than twice the speed of the bus. After 2.5 hours they are 100 miles apart. Find the speed of each.
relative speed*time=relative distance
(7+2B-B)2.5=100
solve for B, then 2B+7
They are going in same direction.
Ty bobpursley
To solve this problem, we can set up a system of equations based on the given information.
Let's assume the speed of the bus is "x" mph.
According to the problem, the speed of the car is 7 mph faster than twice the speed of the bus, which can be represented as "2x + 7" mph.
We know that distance = speed × time. After 2.5 hours, the distance covered by the bus is 2.5x miles, and the distance covered by the car is 2.5(2x + 7) miles.
Since they are 100 miles apart, we can set up the following equation:
2.5x + 2.5(2x + 7) = 100
Now, let's solve the equation:
2.5x + 5x + 17.5 = 100
7.5x + 17.5 = 100
7.5x = 82.5
x = 82.5 / 7.5
x ≈ 11
Therefore, the speed of the bus is approximately 11 mph.
To find the speed of the car, we substitute the value of x back into the expression "2x + 7":
2(11) + 7 = 22 + 7 = 29
Therefore, the speed of the car is 29 mph.
In conclusion, the bus is traveling at approximately 11 mph and the car at 29 mph.