Question

A person takes a trip, driving with a constant speed of 99.0km/h except for a 22.0-min rest stop. The person's average speed is 73.1km/h.

(a) How much time is spent on the trip?

(b) How far does the person travel?

Answer 1

Driving speed $v=99km/hr$

Average speed ,$v_{av}=73.1km/hr$

22 min stop means $22min/60 =0.367hr$

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Time spent on trip =Time spent on driving +time spent on resting

$T=t_{d}+t_{r}$

Speed =Distance/time

Distance =Speed *time

Total distance driven =Driving speed* time spent on driving

$D=v*t_{d}$

$D=99km/hr*t_{d}$

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Average Speed =Total Distance/Total time

$v_{av}=D/T$

$73.1km/hr=(99km/hr*t_{d})/(t_{d}+t_{r})$

$73.1=(99*t_{d})/(t_{d}+0.367)$

$73.1(t_{d}+0.367)=99*t_{d}$

$73.1*t_{d}+73.1*0.367=99*t_{d}$

$73.1*0.367=(99-73.1)*t_{d}$

$73.1*0.367/25.9=t_{d}$

${\color{Red} t_{d}=1.036hr}$

$T=t_{d}+t_{r}=1.036hr+0.367hr$

(a)ANSWER: ${\color{Red} T=1.403hr}$

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(b) How far does the person travel?

$D=v*t_{d}$

$D=99km/hr*1.036hr$

ANSWER: ${\color{Red} D=102.564km}$

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