Question

A car left 30 minutes later than the scheduled time. In order to reach its destination
150km away in time, it has to increase its speed by 25 km/hr from its usual speed. Find
its usual speed.​

Answer 1

Answer:

x be usual speed of the car in km/hr.

The increased speed of car=(x+25) km/hr.

Distance=150km, Time =

Speed

Distance

Let T

1

,T

2

be the time taken by car to cover the given distance in usual time and decreased time.

Given T

1

−T

2

=

2

1

( ∵ ....30 minutes=

2

1

hour )

⇒

x

150

−

x+25

150

=

2

1

⇒

x

1

−

x+25

1

=

300

1

⇒

x(x+25)

x+25−x

=

300

1

⇒x(x+25)=7500

⇒x

2

+25x−7500=0

⇒(x+100)(x−75)=0

⇒x=−100,75

⇒x=75 ....( ∵ x=−100 is not possible )

∴ the usual speed of the car is 75 km/hr

Answer 2

Answer:3/2

Step-by-step explanation:

Let time taken be x.

Speed=distance/time.

Speed=150/x. ------(1)

If car left 30 minutes later,

Time=30min=1/2hr

Speed=150/x+1/2=300/2x+1.----(2)

Car have to incresed speed by 25 km/hr

By given condition,

150/x=300/2x+1 +25.

300x+150=300x+50x^2+25x.

50x^2+25x-150=0

X=-2,X=3/2

Usual speed is 3/2km/hr