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A bicycle travels up a hill at an average speed of 4m/s and down the same hill through the same distance at an average speed of 8m/s. Express the average speed for the entire journey in terms oftandd.

A bicycle travels up a hill at an average speed of 4m/s and down the same hill through the same distance at an average speed of 8m/s. Express the average speed for the entire journey in terms oftandd.

Grade:12

3 Answers

Pushkar Aditya
71 Points
10 years ago
5.333 m/s Average speed is not as we usually do sum of speeds divide by total number of speeds but Average speed is total number of distances divide by total time take let the distance cover by bicycle up a hill be x since distance cover is same in down a hill then Total distance cover during ride is 2x time taken by travel up a hill = x/4 s time taken by travel down a hill = x/8 s total time taken during ride is = x/4 + x/8 =3x/8 Average speed =total distance / total time taken = 2x / (3x/8) = 16x / 3x = 5.333 sec Alter method Simple formula for finding Average speed if distances cover is same is 2uv / (u+v) where u is speed in first ride and v is speed in second ride Acoording to question Average speed = 2 x 4 x 8 / (4+8) = 5.333 sec
Anant Jain
33 Points
10 years ago
5.33 sec
Anant Jain
33 Points
10 years ago
Average speed is (total distances / total time taken) let the distance covered up a hill is x then distance covered down a hill is same to be x then total distances covered = 2x time taken to travel up a hill = x/4 sec time taken to travel down a hill = x/8 sec total time taken during ride = (x/4) + (x/8) = 3x/8 Average speed = total distance / total time taken = 2x / (3x/8) = 16x / 3x = 5. 33 sec Alter method Simplest formula for average speed if distance cover is same is 2uv / (u+v) where u is speed in first ride and v is speed in second ride According to question u= 4 m/s v= 8 m/s putting the value of u and v in 2uv / (u+v) we get 2 x 4 x 8 / (4+8) = 5.33 sec

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