The speed of a moving sidewalk at an airport is 6 ft/sec. A person can walk 42 ft forward on the moving sidewalk in the same time it takes to walk 10 ft on a nonmoving sidewalk in the opposite direction. At what rate would a person walk on a nonmoving sidewalk?
Please help I suck at story problems
42 / (r + 6) = 10 / r
42 r = 10r + 60
No problem! Let's break down the information given in the problem and find a solution step by step.
1. The speed of the moving sidewalk at the airport is 6 ft/sec.
2. A person can walk 42 ft forward on the moving sidewalk in the same time it takes to walk 10 ft on a nonmoving sidewalk in the opposite direction.
To solve the problem, you need to find the rate at which a person would walk on a nonmoving sidewalk.
Let's assume the rate at which a person would walk on a nonmoving sidewalk is "x" ft/sec.
First, we need to calculate the time it takes to walk 42 ft forward on the moving sidewalk. We can use the formula:
Time = Distance / Speed
So, the time taken to walk 42 ft forward on the moving sidewalk would be:
Time_moving_sidewalk = 42 ft / 6 ft/sec
Simplifying the equation:
Time_moving_sidewalk = 7 sec
Now, we need to calculate the time it takes to walk 10 ft on the nonmoving sidewalk in the opposite direction. Again, using the formula:
Time = Distance / Speed
So, the time taken to walk 10 ft on the nonmoving sidewalk would be:
Time_nonmoving_sidewalk = 10 ft / x ft/sec
Now, we can set up an equation based on the given information:
Time_moving_sidewalk = Time_nonmoving_sidewalk
Substituting the values we have:
7 sec = 10 ft / x ft/sec
To solve for "x," we need to isolate it. Multiply both sides of the equation by "x" to get:
7x sec = 10 ft
Divide both sides of the equation by 7 sec to solve for "x":
x = 10 ft / 7 sec
Simplifying the equation:
x ≈ 1.43 ft/sec
Therefore, the rate at which a person would walk on a nonmoving sidewalk is approximately 1.43 ft/sec.
Remember, the key to solving story problems is breaking them down into small steps, identifying the given information, and using equations to find the unknown values.