Ted and Ben took part in the same race. When Ted finnished the race in 25 min., Ben had only run 5/8 of the distance. Ben's average speed was 75m/min SLOWER than Ted's. What is Ted's average running speed?
Speed=Ditance/time
Ted's speed : x m/min
Ben's speed : (x-75)m/min
in 25 minutes:
Ted's distance = 25x
Ben's distance = 25(x-75)
but 25(x-75) = (5/8)(25x)
.
.
.
x = 200
To find Ted's average running speed, we need to calculate the distance he covered. We know that Ted finished the race in 25 minutes.
Let's assume the total distance of the race is 'd'. Since Ben had only run 5/8 of the distance, Ben covered (5/8) * d.
We are also given that Ben's average speed was 75m/min slower than Ted's average speed. So we can write Ben's speed as Ted's speed minus 75 m/min.
Now, let's calculate the distance covered by Ben and equate it to the distance covered by Ted.
Ted's distance = Ben's distance
Ted's speed * Ted's time = Ben's speed * Ben's time
Ted's speed * 25 min = (Ted's speed - 75 m/min) * (5/8) * d
Simplifying the equation,
25 * Ted's speed = (5/8) * d * (Ted's speed - 75)
Now, we can solve this equation for Ted's speed.
25 * Ted's speed = (5/8) * d * Ted's speed - (5/8) * d * 75
25 * Ted's speed - (5/8) * d * Ted's speed = - (5/8) * d * 75
Ted's speed * (25 - (5/8) * d) = - (5/8) * d * 75
Ted's speed = - (5/8) * d * 75 / (25 - (5/8) * d)
Let's say d = 1000 to simplify the calculations.
Ted's speed = - (5/8) * 1000 * 75 / (25 - (5/8) * 1000)
Solving this equation,
Ted's speed = -37500 / (25 - 625)
Ted's speed = -37500 / (-600)
Ted's speed = 62.5 m/min
Therefore, Ted's average running speed is 62.5 m/min.