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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?

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?

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
6 years ago
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 \Deltat) by the vehicle under the increased speed limit is given as:
236-1848_delta.JPG
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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