Tom and Jerry took part in a race. Both boys started running at the same time. After 4 hours, Tom had completed the race but Jerry had covered only 4/5 of the route. If Jerry's average speed was 2km/h less than Tom's, find the length of the route.
distance = speed * time, so if Tom's speed is s, his distance was 4s. For Jerry,
(4/5)(4s) = 4(s-2)
solve for s, and then you can get the distance: 4s
Tom's speed = X km/h.
Jerry's speed = x-2 km/h.
Tom: d = x * t. = 4x.
Jerry: 4d/5 = (x-2)*t
d = (1.25x - 2.5)t
d = (1.25x - 2.5)4
d = 5x - 10.
d = 4x = 5x - 10
4x = 5x - 10
X = 10 km/h.
d = 10km/h * 4h = 40 km. = Length of the route.
To find the length of the route, we can start by determining Tom's speed.
Let's assume that Tom's speed is "x" km/h.
Since Tom completed the race in 4 hours, we can calculate the distance covered by him using the formula: Distance = Speed * Time.
So, Tom's distance = x km/h * 4 hours = 4x km.
Now, let's find Jerry's speed.
Since Jerry's average speed was 2 km/h less than Tom's, Jerry's speed would be (x - 2) km/h.
Jerry only covered 4/5 of the route after 4 hours, so we can calculate the distance covered by Jerry: Distance = Speed * Time.
Jerry's distance = (x - 2) km/h * 4 hours = 4(x - 2) km.
According to the given information, Jerry's distance is 4/5 of the total route length.
Therefore, 4(x - 2) = 4/5 * (4x).
Simplifying the equation:
4x - 8 = 16x/5
Multiply both sides by 5 to eliminate the fraction:
20x - 40 = 16x
Subtract 16x from both sides:
4x = 40
Divide both sides by 4:
x = 10
Now that we have Tom's speed (x = 10 km/h), we can find the length of the route using Tom's distance formula: Distance = Speed * Time.
Distance = 10 km/h * 4 hours = 40 km.
Therefore, the length of the route is 40 km.