Math question in description

Question

Bob travels in an airplane a distance of 1200 km. For one-fourth of the distance, the airplane flies at a speed of 840 km/h, and for the rest of the distance, it flies at a speed of 600 km/h.  How long does the trip take?

Answer 1

Use the formula: distance = rate x time

 

For 1/4 of the distance, the plane will have traveled (1/4) * 1200 = 300 km

 

Using the above formula and letting t₁ represent the time traveled, we have the following equation:

 

300 = 840t₁

 

The remainder of the distance will be 1200 - 300 = 900 km. Let t₂ = the time traveled for this leg of the flight. For this portion of the trip, we have this equation:

 

900 = 600t₂

 

Solving for t₁ gives us t₁ = 300/840 = 5/14 of an hour

 

Solving for t₂ gives us t₂ = 900/600 = 3/2 = 1.5 hours

 

The entire trip will take t₁ + t₂ = 5/14 + 3/2 = 5/14 + 21/14 = 26/14 = 13/7 = 1 6/7 hours.