A bicyclist covered

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)

1.

let the route length = x miles

covered distance = 5/7 x +40

yet to cover = 118-0.75 = 117.25

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)

2. 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

distance e= speed * time ; since the distance traveled is same therefore

(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)

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