DRT problem

A bicyclist travels 20 miles per hour faster than a walker. The cyclist traveled 25 miles in the time it took the walker to walk 5 miles. Find their speeds.

let speed of walker be x mph

then speed of biker is x+20
so 25/(x+20) = 5/x

cross-multiply and solve for x
(you should get x = 5)

To solve this problem, we'll use the DRT formula, which stands for Distance equals Rate multiplied by Time.

Let's assume the speed of the walker is x miles per hour. Since the bicyclist travels 20 miles per hour faster than the walker, the speed of the cyclist would be x + 20 miles per hour.

Given that the walker walked a distance of 5 miles, we can set up the following equation using the DRT formula:

Distance = Rate x Time

For the walker:
5 = x * t

For the cyclist:
25 = (x + 20) * t

Since both the walker and the cyclist took the same amount of time, we can set the two equations equal to each other:

5 = x * t
25 = (x + 20) * t

Now we need to solve this system of equations. We can rearrange the first equation to solve for t:

t = 5 / x

Substituting this value for t in the second equation, we get:

25 = (x + 20) * (5 / x)

Now we can solve for x by cross multiplying:

25x = 5(x + 20)

Simplifying:

25x = 5x + 100

Subtracting 5x from both sides:

20x = 100

Dividing both sides by 20:

x = 5

So, the speed of the walker is 5 miles per hour. To find the speed of the cyclist, we can substitute this value back into the original equation:

Speed of cyclist = Speed of walker + 20
= 5 + 20
= 25

Therefore, the speed of the cyclist is 25 miles per hour.