Two cyclists leave from an intersection at the same time One

Two cyclists leave from an intersection at the same time. One travels due north at a speed of 18 18 mph, and the other travels due east at a speed of 24 24 mph. How long until the distance between them is 60 60 miles?

The current of a river is 33 miles per hour. A boat travels to a point 88 miles upstream and back in 22 hours. What is the speed of the boat in still water?

A water tank can be filled by an inlet pipe in 88 hours. It takes 33 times as long for the outlet pipe to empty the tank. How long will it take to fill the tank if both pipes are open?

Solution

Sol.1- both cyclist move in their respective directions. who travels in north direction covers 36 miles in 2 hours and who travels in east direction covers 48 miles in 2 hours. if we apply pythagoras theorem i.e.

(base)² + (height)² = (hypotenuse)²

   (36)² + (48)² = (hypotenuse)²

  i.e. hypotenuse = 60 miles

so duration for becoming distance between two cyclist is 60 miles is 2 hours.

Sol.2- let speed of boat = x mph

current of river water = 33 mph

then speed in upstream = x-33

and speed in down stream = x+33

time = distance / speed

time upstrem + time downstream = 22 hours

22 = 88/(x-33) +88/(x+33)

1/4 = 2x/(x²-33²)

x²- 8x- 1089=0

after solving this quadratic equation we accept the postive value of x i.e. 37.24 mph.

Sol.3- water tank filled by inlet pipe in one hour = 1/88 part

and water tank empty by outlet pipe in one hour =1/(88*33)

then time taken to fill the tank if both pipes are open is

= (1/88)-(1/(88*33))

= (1/88)(32/33)

= 4 / 363

= 363/4 hours or 90 hours 45 min to fill the tank.