a cyclist bikes at a constant speed for 19 mile. He then returns home at the same speed but takes a different route. His return trip takes one hour longer and is 24 miles. Find his speed
since time = distance/speed,
24/s = 19/s + 1
To find the cyclist's speed, we can use the formula: Speed = Distance / Time.
Let's assume the cyclist's speed is "s" miles per hour.
On the first leg of the journey, the cyclist travels a distance of 19 miles at a speed of "s". Therefore, the time taken for this leg can be calculated as Time1 = Distance1 / Speed = 19 miles / s mph.
On the return trip, the cyclist travels a distance of 24 miles at the same speed "s", but it takes one hour longer. Therefore, the time taken for the return trip can be calculated as Time2 = Distance2 / Speed = 24 miles / s mph.
We are given that Time2 is one hour longer than Time1, so we can write the equation: Time2 = Time1 + 1 hour.
Substituting the values, we get 24 miles / s mph = 19 miles / s mph + 1 hour.
To solve this equation, we can simplify it by getting rid of the fractions. We can do this by multiplying both sides of the equation by "s" to cancel out the denominators, resulting in:
24 miles = 19 miles + s hour.
Now, we can isolate "s" to find the speed of the cyclist:
s hour = 24 miles - 19 miles.
s hour = 5 miles.
Therefore, the cyclist's speed is s = 5 miles per hour.