Question

Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed?

Answer 1

Answer:

V = 20 miles /sec

Explanation:

We have remaining distance   =  d  = 96 miles

Lets call  Pascal velocity  V in miles per hour

Now if he increases his velocity by  50 % (equivalent to multiply by 1.5 ) he will need a time t₁ to arrive then as V = d/t

1.5* V  = d/ t₁      ⇒   1.5 * V  =  96 /t₁

And in the case of reducing his velocity

(V / 4) = d/ (t₁ + 16 )     ⇒  V * (t₁ + 16 ) = 4*d     ⇒ V*t₁ + 16*V = 384

So we a 2 equation system with two uknown variables

1.5*V = 96/t₁      (1)

V*t₁  + 16*V = 384     (2)

We solve  from equation    (1)      t₁  = 64/V

And by substitution   in equation (2)

V * (64/V) + 16* V = 384

64  + 16 *V  = 384         ⇒   16*V = 320      ⇒  V= 320/16

V = 20 miles /sec