If Greg is 1.7 times faster than Owen, it means that he will take a 1/1.7 part of the time Owen needs to clean a window. Meaning, it takes Greg 1/(1.7) =0.59 of the time Owen takes to clean one window.
If the time required to clean one window by Owen is T and it's 1.7 times faster than Owen, the time Greg takes to clean one window is 0.59T.
The two can clean a window together in (1/T + 1/0.59T)^-1 = 1 minute.
If they clean 100 windows together in 39 minutes, each window takes 39/100 = 0.39 minutes.
If we solve the rational equation 0.39 = (1/T + 1/0.59T)^-1 for T, we'll find the time it takes for Owen to clean one window, so let's multiply the equation by T*0.59 to get 0.39T*0.59 = 1 + 0.59, and subtract 0.59 from both sides of the equation to get 0.39T*0.59 - 0.59 = 1.
If we divide by 0.39, we'll find that T = 1/(0.39*0.59) = 2.7 minutes.
If we multiply by 100 the time it takes for T to clean ONE window, we can find out how long it would take T to clean 100 windows. Therefore, T = 100 * 2.7 = <<100*2.7=270>>270 minutes. Answer: \boxed{270}.
Greg is 1.7 times faster at cleaning windows than Owen. It takes 39 minutes for them to clean 100 windows together. Using a rational equation, calculate how long it would take Owen to clean 100 windows by himself. Round the answer to the nearest tenth.
1 answer