The legal speed limit on a highway is changed from 55 mi/h (=88.5 km/h) to 65 mi/h (=104.6 km/h). How much time is thereby saved on a trip from the Buffalo entrance to the New York City exit of the New York State Thruway for someone traveling at the higher speed over this 435-mi (=700-km) stretch of highway?

Question

Aditi Chauhan · Answer

Given:
Initial speed limit of highway, v₁ = 55 mi/ h.
Final speed limit on highway, v₂ = 65 mi /h
Stretch of highway, s = 435 mi.
Let us assume that the time taken by the vehicle to travel a distance s on the highway with speed v₁ is t₁.
Therefore the time t₁ can be given as:

$t_{1} = \frac{s}{v_{1}}$
Substitute the given values, to have
$t_{1} = \frac{435\ mi}{55\ mi/h}$
$= 7.90\ h$
Therefore the time taken by the vehicle to go 435 mi on highway with initial speed limit is 7.90 h.
Let us assume that the time taken by the vehicle to travel a distance s on the highway with speed v₂ is t₂.
Therefore the time t₂ can be given as:
$t_{2} = \frac{s}{v_{2}}$
Substitute the given values, to have
$t_{2} = \frac{435\ mi}{65\ mi/h}$
= 6.69 h
Therefore the time taken by the vehicle to go 435 mi on highway with increased speed limit is 6.69 h.
The amount of time saved (say $\Delta$ t) by the vehicle under the increased speed limit is given as:

Rounding off to two significant figures, we have
$\Delta = 1.2 h$
Therefore the time saved due to increased speed limit is 1.2 h.

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