Question

A plane left 30 minute later then the schedule
time and in order to reach its destination
1500 km away, in time it has to increase it
its
speed by 250 I krolher from its usual
Find 'its usual spied I work out of home]
Ans: 750km/hr​

Answer 1

Given:

A plane left 30 minutes later than the schedule  time and in order to reach its destination  1500 km away, in time it has to increase its  speed by 250 km/hr from its usual speed

To find:

It's usual speed

Solution:

Let's assume,

"s" km/hr → usual speed of the plane

"t" hr → usual time of the plane

We know,

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

In order to reach in time i.e., t, the plane needs to increase its speed by 250 km/hr, so we can from the equation as:

$t = \frac{1500}{s + 250 }$ ..... (i)

With its usual speed, the plane reaches its destination 30 minutes later, so we can from the equation as:

$t + \frac{30}{60} = \frac{1500}{s }$ ..... (ii)

On substituting (i) in (ii), we get

$\frac{1500}{s } - \frac{1500}{s + 250 } = \frac{30}{60}$

$\implies 1500 [\frac{1}{s } - \frac{1}{s + 250 }] = \frac{1}{2}$

$\implies 1500 [\frac{s + 250 - s}{s(s + 250) } ] = \frac{1}{2}$

$\implies 1500 [\frac{250}{s^2 + 250s } ] = \frac{1}{2}$

$\implies s^2 + 250s - 750000 = 0$

$\implies s^2 + 1000s - 750s - 750000 = 0$

$\implies s (s + 1000) - 750 (s + 1000) = 0$

$\implies (s + 1000)(s - 750) = 0$

since speed cannot be in negative therefore ignoring the negative value

$\implies \bold{s = 750 \:km/hr}$

Thus, the usual speed of the plane is → 750 km/hr.

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