Question

Fred runs at average speed of 12km per hour and flies at an average speed of 76km per hour. They traveled a total distance of 120 km in 2 hours How long did it take her to run and fly

Answer 1

Fred ran for 0.5 hours and flied for 1.5 hours.

Explanation:

Distance covers while running = d

Time taken to cover d distance = x

Speed while running = 12 km/h

`12 km/h=(d)/(x)`

`d=12km/h* x`

Distance covers while flying = D

Time taken to cover D distance = y

Speed while running = 76 km/h

`76km/h=(D)/(y)`

`D=76 km/h* y`

Total distance = 120 km

Total time taken = 2 hours

Average speed :
`\fracd{120 km}{2 hour}=60 km/h`

Here ,120 km = d + D

120 km = d + D

`120 km= 12 km/h* x+76 km/h* y`

`12x+76y=120`..[1]

x + y = 2 hours..[2]

Solving both equation by substitution method:

Putting value of x from [2] in [1]:

x = 2 - y

`12x+76y=120`

`12(2-y)+76y=120`

`y=(120-24)/(76-12)=1.5`

x = 2 - y = 2 - 1.5 = 0.5

Fred ran for 0.5 hours and flied for 1.5 hours.