Question

A person takes a trip, driving with a constant speed of 99.5 km/h, except for a 22.0-min rest stop. If the person's average speed is 77.0 km/h, find the following. (a) How much time is spent on the trip? h (b) How far does the person travel? km

Answer 1

Given average speed,$v_{av}=77km/hr$

Total time taken for trip =Time for driving +Time for rest = $t_{d}+t_{s}$

Given time for rest =22min =$22min/60 =0.367hr$

$t_{s} =0.367hr$

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Let d be the total distance covered

Speed =Distance /Time

$99.5km/hr=d/t_{d}$

$d=99.5*t_{d}$

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Average speed =Total distance/Total time

$v_{av}=\frac{d}{t}$

$v_{av}=\frac{99.5*t_{d}}{t_{d}+t_{s}}$

$77=\frac{99.5*t_{d}}{t_{d}+0.367}$

$77(t_{d}+0.367)=99.5*t_{d}$

$77t_{d}+77*0.367=99.5t_{d}$

$77*0.367=(99.5-77)t_{d}$

$t_{d}=77*0.367/22.5$

$t_{d}=1.256hr$

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Total time taken for trip =Time for driving +Time for rest = $t_{d}+t_{s}=1.256hr+0.367hr$

ANSWER: ${\color{Red} t=1.623hr}$

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(b) How far does the person travel?

$d=99.5*t_{d}$

$d=99.5*1.256hr$

$d=124.972km$

ANSWER : ${\color{Red} d=125km}$

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Answer 2

SOLUTION :

a.

Let time of travel be t hr and distance covered be d km.

Rest time = 22 min = 22/60 =  0.3667 hr.

So, 

d = 99.5 * (t - 0.3667) 

Also, d = 77 * t

So,

99.5 (t - 0.3667) = 77 t

=> 99.5 t - 36.4866 = 77 t

=> 99.5 t - 77 t = 36.4866

=> 22.5 t = 36.4866

=> t = 36.4866 / 22.5 = 1.6216 hr = 1 hr 37 min 18 sec approx. (ANSWER).

b.

d = 77 * 1.6216 = 124.86 km approx. (ANSWER).