Question

Consider the following word problem:Two planes, which are 1180 miles apart, fly toward each other. Their speeds differ by 40 mph. If they pass each other in 2 hours,what is the speed of each?Step 1 of 2: Use the variable x to set up an equation to solve the given problem. Set up the equation, but do not take steps to solve it.

Answer 1

So we have two planes flying toward each other. Let's use v for the speed of the slower plane. Then the speed of the faster plane is v+40. If we pass to the reference system of the slower plane we have that its speed is 0 and the speed of the other plane is v+v+40=2v+40. So basically we have a problem where one of the planes is stationary whereas the other approaches at 2v+40mph and it takes it 2 hours to travel 1180 miles. Remember that the speed is equal to the distance traveled divided by the time it took the plane to travel that distance. Then we get:

`\begin{gathered} 2v+40(mi)/(h)=(1180mi)/(2h)=590(mi)/(h) \\ 2v=590(mi)/(h)-40(mi)/(h)=550(mi)/(h) \\ v=(550(mi)/(h))/(2)=275(mi)/(h) \end{gathered}`

Then we get:

`v+40(mi)/(h)=275(mi)/(h)+40(mi)/(h)=315(mi)/(h)`

Then the speeds of the planes are 275mph and 315mph.