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.