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# ive been stuck for a hour help please

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Sarah walked 10 km into the country. She returned walking 3 km/h slower. The total time for the
trip was 7 hours. How fast did she walk going out to the country?

May 29, 2020

#1
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Let v be speed in km/hr on outward journey.

Outward time:  10/v hr

Return time: 10/(v - 3) hr

Total time:  10/v + 10/(v - 3) = 7

Can you take it from here?

May 29, 2020
edited by Alan  May 29, 2020
#2
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$$x = {v*t}$$

Vi = initial velocity

T= second time

T= first time

$$10= {Vi* Ti}$$

$$10 = {(Vi-{3km\over h}(tf))}$$

$$Vi*Ti= {(Vi- { 3km\over h}})*tf$$

$$Tf = {7h-Ti}$$

$$Vi*Ti = (Vi-{3km\over h})*(7h-Ti)$$

$$Vi*Ti = ({Vi*7h-ViTi-{3km\over h}}+{3km \over h}*Ti)$$

$$Vi*Ti= {7h*Vi - 21km + {3km\over h}}*Ti$$

$$20km = {7h*Vi - 21km +{ 3km\over h}}*Ti$$

$$41km ={ {70km*h+ { 3km\over h}}*Ti^2\over Ti}$$

$$41km ={ {7h*10km \over Ti}+{3km*Ti\over h}\over Ti}$$

$$0={ {3km*Ti^2\over h} - 41km*Ti+70 km*h }$$

$$0 = {3x^2 -41 x + 70 }$$

This equation gives us two answers:

2 = the number of hours in the initial trip

How fast did she walk going out to the country?

$$5km\over h$$

May 29, 2020