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Brandon and Pat drove from Edmonton to Saskatoon, a distance of 545km. Brandon drove the first part of the trip at an average speed of 100 km/h and Pat drove the remainder at an average speed of 90 km/h. If the trip took Brandon and Pat 5.75 h, determine the number of hours each drove. 

 Dec 30, 2020
edited by Guest  Dec 30, 2020
 #1
avatar+11238 
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Brandon and Pat drove from Edmonton to Saskatoon, a distance of 545km. Brandon drove the first part of the trip at an average speed of 100 km/h and Pat drove the remainder at an average speed of 90 km/h. If the trip took Brandon and Pat 5.75 h, determine the number of hours each drove. 

 

Hello Guest!

 

\(\color{blue}v_B\cdot t_B+v_P\cdot t_P=545\\ 100\cdot t_B+90\cdot t_P=545\\ \color{blue}t_B+t_P=5.75\\ t_B=5.75-t_P\)

\(100\cdot (5.75-t_P)+90\cdot t_P=545\\ 575-100t_P+90t_P=545\\ -10t_P=545-575\\ 10t_P=30\\ \color{blue}t_P=3\ h \)

\(t_B=5.75-t_P\\ t_B=5.75-3\)

\(t_B=2.75\ h\)

laugh  !

 Dec 31, 2020
 #2
avatar+536 
+1

I got that Pat drove 3 hours and Brandon drove the rest.

If Bradon drove the entire way, then he would have drove 575 miles. 

But for each hour Pat drives, that amount decreases by 10 miles.

To get our result, we subtract 545 from 575 to get 30 and divide by 10 to get that pat drove 3 miles

Checking our work, 3*90 is 270 and 2.75*100 is 275. 270+275 is 545.

 Dec 31, 2020

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