Two planes, 2000 miles apart, fly toward each other. Their speeds differ by 35 mph. If they pass each other in 3 hours, what is thespeed of each?

Question

Two planes, 2000 miles apart, fly toward each other. Their speeds differ by 35 mph. If they pass each other in 3 hours, what is thespeed of each?

Answer 1

Judy,

 

Let the speed of one plane = v and the speed of the other = v + 35 mi/h.  Both planes have been flying for the same amount of time when reach each other, so since distance = velocity x time:

 

1st plane D(1) = v·t

2nd plane D(2) = (v+35)·t

 

and D(1) + D(2) = 2000

 

Putting this all together:

 

v·t + (v+35)·t = 2000

 

2v + 35 = 2000/t= 666.7 mi/h

 

2v = 666.7 mi/h = 35 mi/h = 631.7 mi/h

 

v₁ = (631.7/2) mi/hr = 315.8 mi/h ≈ 316 mi/h (1st plane)

 

v₂ = (316 + 35) mi/h = 351 mi/hr (2nd plane)

 

Check:

 

(316x3)mi/h + (351x3)mi/hr = 948 mi/h + 1053 mi/h = 2001 mi/h ≈ 2000 mi/h

 

where we gained 1 mi/h due to round-off errors.