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Algebra
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A bicyclist covered 

5
7


 of his route and an additional 40 miles. He has yet to cover 118 miles less than 0.75 of his route. How long is his route?



It takes 4.5 hours for a ship moving downriver to get from port A to port B. The return journey takes 6.3 hours. The river flows at 40 meters per minute. What is the distance between the two ports? (Give your answer in kilometers. 1 km = 1,000 meters)

Apr 4th, 2015

. Question 1 :

Let the route length  = x miles 

covered distance = 5/7 x +40

distance yet to cover = 118-0.75 = 117.25

total route distance = covered + uncovered distance

x =  (5/7)x +40 +117.25

solving we get , x  - 5/7 x  = 157.25  ;  2/5 x = 157.25

or  x = 157.25 * 2/5 = 393.125 miles  (answer)

Question -2 : It takes 4.5 hours for a ship moving downriver to get from port A to port B. The return journey takes 6.3 hours. The river flows at 40 meters per minute. What is the distance between the two ports? (Give your answer in kilometers. 1 km = 1,000 meters)

Let the speed of ship is x meters/minute

when ship is traveling  along the steam , speed will become (x+40)     time needed 4.5 hrs =  270 minute 

when ship is traveling  against the steam , speed will become (x-40)     time needed 4.5 hrs =  390 minute 

we know that ,   distance = speed * time  ; 

since the distance traveled is same by ship is equal both sides therefore ,  we can equate them 

Distance downstream = distance upstream

(x+40) 270 = (x-40) 390

solving ( x+40) 9 =(x-40)13

or, 9x+360 = 13x-520

or, 4x = 880

hence x = 880/4 = 220 meter per minute 

hence distacne beteeen ports = (x+40)*270 =(220+40) * 270 =70200 meters  or 70.2 km  (answer)


Apr 4th, 2015

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