# Math Help - we gotta problem here guys=("tough Question"

1. ## we gotta problem here guys=("tough Question"

Hi
I'm new and it's my first post
anyways can anyone help me to solve this Question it's really annoying

How fast?

Thanks

2. Originally Posted by User Name
Hi
I'm new and it's my first post
anyways can anyone help me to solve this Question it's really annoying

How fast?

A spacecraft undergoes a journey of two separate legs. The second leg is twice as long as the first leg, and the average speed of the craft during the second leg is is 10% higher than its average speed during the earlier leg.
The spacecraft's average speed over the entire journey is 9660 km/h.
calculate its average speed for each leg.

Thanks
Let the average speed in first leg be v and let distance of first leg be x.

Then average speed in second leg is v + (v/10) = 11v/10 and distance of second leg is 2x.

Time to travel first leg: $t_1 = \frac{x}{v}$ .... (1)

Time to travel second leg: $t_2 = \frac{2x}{11v/10} = \frac{20 x}{11 v}$ .... (2)

Average speed for entire journey: $9660 = \frac{3x}{t_1 + t_2}$ .... (3)

Substitute (1) and (2) into (3) and solve for v (note that the x's cancel out).

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