Word problem

Question

a jet plane traveling 450 mph overtakes a propeller plane traveling at 250 mph that had a three hour head start. how far from thr starting points are thr planes?

Answer 1

D = distance = velocity x time 

 

Let t10 = starting time of prop plane = 0 hr    (select reference time = 0)

 

      t20 = starting time of jet plane = 3 hr + t10 = 3 hr

 

      v1 = prop plane velocity = 250 mph

 

      v2 = jet plane velocity = 450 mph

 

      t = time when jet plane meets (or overtakes) the prop plane

 

D = distance = velocity x time = v1*(t - t10) = v2*(t - t20)

 

Solve for t:

 

v1*t - v1*t10 = v2*t - v2*t20         (combine like terms)

 

t*(v2 - v1) = v2*t20 - v1*t10

 

t = (v2*t20 - v1*t10)/(v2 - v1) = (450*3 - 0)/(450 - 250) = 1350/200 = 6.75 hr  when jet overtakes prop plane

 

Now plug in values for prop plane (or jet plane) to find distance when jet overtakes prop:

 

D = v1*(t - t10)  = v1*t  =  250 mph x 6.75 hr = 1,687.5 miles

 

checking with jet plane:

 

D = v2*(t - t20) = 450 mph*(6.75 - 3)hr = 1,687.5 miles

 

so it takes the jet 3.75 hr to fly the same distance as the prop plane takes in 6.75 hr