Question

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes 6 hours and 24 minutes, but when there is a wind blowing from Penthaven to Jackson at 50 miles per hour, the trip takes 6 hours and 40 minutes. How many miles is the distance from Penthaven to Jackson?

(Assume that the plane flies at a constant speed, and that the turnaround time is negligible.)

Answer 1

Answer:800 miles

Explanation:

Given

Round trip for Penthaven to Jackson takes 6 hr and 24 minutes in absence of wind

`t_1=6+(24)/(60)=6.4\ hr`

When Wind blows from Penthaven to Jackson it takes 6 hr and 40 min i.e.

`t_2=6+(40)/(60)=(20)/(3)\ hr`

Speed of wind
`v=50\ mph`

Suppose x be the distance between Penthaven and Jackson and u be the speed of plane

So initially

`6.4=(x)/(u)+(x)/(u)`

`6.4=(2x)/(u)`

`x=3.2u \quad \ldots(i)`

When wind is blowing then,

`\Rightarrow (20)/(3)=(x)/(u+v)+(x)/(u-v)`

`\Rightarrow (20)/(3)=x[(1)/(u+50)+(1)/(u-50)]`

`\Rightarrow (20)/(3)=x[(2u)/(u^2-50^2)]\quad \ldots(ii)`

Substitute the value of x in
`(ii)`

`\Rightarrow (20)/(3)=(2u[3.2u])/(u^2-50^2)`

`\Rightarrow 10[u^2-50^2]=9.6u^2`

`\Rightarrow 0.4u^2=50^2* 10`

`\Rightarrow u^2=(50^2* 10^2)/(4)`

`\Rightarrow u=250\ mph`

Thus
`x=3.2* 250=800\ miles`