What is the speed of each planes.

Question

Two planes, which are 1880 miles apart, fly toward each other. Their speeds differ by 40mph. If they pass each other in 2 hours, what is the speed of each?

Answer 1

Suppose the slow one starts from the left and moves right at speed v, and the fast one starts from the right and moves left at speed v + 40.  They meet at distance x from the left at time t = 2 hours.  Then

 

vt = x

(v + 40)t = 1880 - x

 

t = 2

x = vt = 2v

 

(v + 40)(2) = 1880 - 2v

2v + 80 = 1880 - 2v

4v = 1800

v = 1800/4 = 450

v + 40 = 450 + 40 = 490

 

Slow plane:  450 miles/hour

Fast plane:   490 miles/hour