Rate Problem:
Mr. Stewart rode a distance of 12miles out into the country on a bicycle and returned on foot. His rate on the bicycle was 4 times his rate on foot. He spent 5 hours on the entire trip. Find the rate of walking and on the bicycle.
Mr. Stewart rode a distance of 12miles out into the country on a bicycle and returned on foot. His rate on the bicycle was 4 times his rate on foot. He spent 5 hours on the entire trip. Find the rate of walking and on the bicycle.
Letting V equal the walking speed,
12/4V + 12/V = 5
Solve for V.
To solve this rate problem, let's assign variables to the rates of walking and bicycling. Let's say Mr. Stewart's rate on foot is "x" miles per hour, and his rate on the bicycle is "4x" miles per hour.
Since we know the distance he traveled and the rates, we can set up an equation using the formula: Time = Distance / Rate.
The time spent on the bicycle can be calculated by dividing the distance (12 miles) by the rate on the bicycle (4x miles per hour): Time on Bicycle = 12 miles / (4x miles per hour) = 3 hours.
The remaining time spent walking is given as 5 hours total - 3 hours on the bicycle = 2 hours.
Using the formula Time = Distance / Rate, we can now set up the equation for the time spent walking: 2 hours = 12 miles / (x miles per hour).
To find the rate of walking, we can rearrange the equation: x = 12 miles / 2 hours = 6 miles per hour.
Therefore, Mr. Stewart's rate of walking is 6 miles per hour, and his rate on the bicycle is 4 times that, which means the rate on the bicycle is 24 miles per hour.