Question

A person takes a trip, driving with a constant speed of 99.5 km/h, except for a...

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

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Answer #1

Given average speed,av-77km/hr

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

Given time for rest =22min =22min/600.367hr

ts = 0367hr

================

Let d be the total distance covered

Speed =Distance /Time

99.5km/hr-d/td

d = 99.5* td

===============

Average speed =Total distance/Total time

Vau-

99.5* td Vau,-- ta +t,

99.5* td 0.367 77=

77(4 + 0.367) = 99.5 * td

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

77 * 0.367 (99.5-77Ma

t_{d}=77*0.367/22.5

t_{d}=1.256hr

==============

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}

================

(b) How far does the person travel?

d = 99.5* td

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).

answered by: Tulsiram Garg
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