##### The tour bus has traveled the Xirst half of your trip at only 30 mph. How fast w

 Algebra Tutor: None Selected Time limit: 1 Day

The

tour

bus

has

traveled

the

first

half

of

your

trip

at

only

30

mph.

How

fast

would

your

tour

bus

have

to

travel

for

the

rest

of

your

trip

to

have

an

average

speed

of

50

mph?

Jun 19th, 2015

Let the speed in the second half of the trip be x.

Let the total distance be d.

Let the time taken for the first half of the trip be t

and the time taken for the first half of the trip be t' .

We know that

$\\ Speed=\frac{Distance}{Time}\\ \\or\\ \\ Time=\frac{Distance}{Speed}\\$

For the first half of the trip,

Distance = d/2

Speed = 30 mph

Time = t

So,

$\\ t=\frac{d/2}{30}\\ \\ t=\frac{d}{2\times30}\\ \\ t=\frac{d}{60}\\$

For the second half of the trip,

Distance = d/2

Speed = x

Time = t'

So,

$\\ t'=\frac{d/2}{x}\\ \\ t'=\frac{d}{2x}\\$

Total time taken for the trip = t + t' = $\\ \frac{d}{60}+\frac{d}{2x} =\frac{dx+30d}{60x}$

It is required that average speed for the trip be 50 mph.

So, again using the formula for speed, we get

$\\ 50=\frac{d}{\frac{dx+30d}{60x}}\\ \\ 50=\frac{d\times60x}{dx+30d}\\ \\ 50=\frac{d\times60x}{d(x+30)}\\ \\ 50=\frac{60x}{x+30}\\ \\ 50(x+30)=60x\\ \\ 50x+1500=60x\\ \\ 60x-50x=1500\\ \\ 10x=1500\\ \\ x=\frac{1500}{10}\\ \\ x=150$

So the bus should travel at 150 mph for the second half of the trip.

Jun 19th, 2015

this is not correct

Jun 19th, 2015

lol yes it is, apologies and thank you:]

Jun 19th, 2015

You are welcome :)

Jun 19th, 2015

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Jun 19th, 2015
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Jun 19th, 2015
Dec 9th, 2016
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