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?

Question

Physics

Casey Waller

27 January, 01:09

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?

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Answers (1)

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Faith Case · Answer 1

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