Question

two planes make a 600 mile flight,one flying 50mph faster than the other.of the slower plane takes 2hours longer,what is the rate of its plane?

Answer 1

Given:

Two planes make a 600-mile flight,

One flying 50mph faster than the other.

Of the slower plane takes 2hours longer

To find:

What is the rate of its plane?

Solution:

Let "S mph" represents the speed of the slower plane.

So, "(S + 50) mph" represents the speed of the faster plane.

Total distance travelled by the planes = 600 miles

We know,

$\boxed{\bold{Time = \frac{Distance}{Speed} }}$

Therefore,

The time taken by the slower plane = $\frac{600}{S}$

The time taken by the faster plane = $\frac{600}{S \:+ \:50}$

Now, according to the question, we can form an equation as,

$\frac{600}{S} - \frac{600}{S \:+ \:50} = 2$

$\implies 600 [\frac{1}{S} - \frac{1}{S \:+\:50} ] = 2$

$\implies 600 [\frac{S\:+\:50 \:-\:S}{S(S\:+\:50)}] = 2$

$\implies 300 [\frac{\:50 \:}{S(S\:+\:50)}] = 1$

$\implies S(S\:+\:50) = 15000$

$\implies S^2\:+\:50S = 15000$

$\implies S^2\:+\:50S - 15000 = 0$

$\implies S^2 + 150S - 100S - 15000 = 0$

$\implies S(S + 150) - 100(S + 150) = 0$

$\implies (S + 150)(S - 100) = 0$

$\implies S = - 150\:or\:S = 100$

since the value of speed cannot be negative, so ignoring the negative value, we get

$\implies \bold{S = 100\:mph}$ ← speed of the slower plane

∴ Speed of the faster plane = S + 50 = 100 + 50 = 150 mph

Thus, the rate of its plane are:

$\boxed{\bold{The \:speed\:of\:the\:slower\:plane\:is\:\underline{100\:mph}}}.\\\\\boxed{\bold{The \:speed\:of\:the\:faster\:plane\:is\:\underline{150\:mph}}}.$

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