Question

Saktiman covered a total distance of 670 km by travelling 9 hours by bus and 4 hours by
taxi meanwhile Arjun travelled 7 hours by taxi and 8 hours by bus covering a distance of
785 km. Find the speed of the taxi and the bus if the speeds of the 2 buses were same and
the speeds of both taxi are same

Answer 1

Answer:

The Speed of the bus = 50 kmph

The Speed of the taxi = 55 kmph

Step-by-step explanation:

Given;

Speed of the two Taxis are equal;

And Speed of the two Buses are equal.

Let the Speed of the Bus = S1

Let the Speed of the Taxi = S2

Saktiman:

The distance covered by Saktiman ($D_{s}$) = 670 km

He used two means of transport.

$D_{s}$1 = Speed of the bus x Time

   = S1 x 9

$D_{s}$2 = Speed of the taxi x Time

   = S2 x 4

$D_{s}$ = $D_{s}$1 + $D_{s}$2

=> 9S1 + 4S2 = 670   ------- Eq(1)

Arjun:

The distance covered by Arjun ($D_{a}$) = 785 km

He used two means of transport.

$D_{a}$1 = Speed of the Taxi x Time

   = S2 x 7

$D_{a}$2 = Speed of the Bus x Time

   = S1 x 8

$D_{a}$ = $D_{a}$1 + $D_{a}$2

=> 8S1 + 7S2 = 785   ------- Eq(2)

Solving Eq(1) & Eq(2):

9S1 + 4S2 = 670      x 7

8S1 + 7S2 = 785      x 4

  63S1 + 28S2 = 4690

  32S1 + 28S2 = 3140

 (-)  (-)     (-)  

  ------------------

  31S1 = 1550

 => S1 = 50 km/hr

From Eq(2);

8S1 + 7S2 = 785

8(50) + 7S2 = 785

=> 7S2 = 785 - 400

=> 7S2 = 385

=> S2 = 55 km/hr

Therefore,

The Speed of the bus S1 = 50 kmph

The Speed of the taxi S2 = 55 kmph

Answer 2

Answer:

The Speed of the bus X= 50 kmph

The Speed of the taxi Y = 55 kmph

Step-by-step explanation:

In this question

We have been given that

Speed of the two Taxis are equal;

And Speed of the two Buses are equal.

Let the Speed of the Bus = X

Let the Speed of the Taxi = Y

Saktiman:

The distance covered by Saktiman  = 670 km

He used two means of transport.

Distance Covered by bus = Speed of the bus x Time

  = X x 9

Distance covered by taxi = Speed of the taxi x Time

  = Y x 4

Total Distance

=> 9X + 4Y = 670   -------(i)

Arjun:

The distance covered by Arjun = 785 km

He used two means of transport.

Distance covered by Taxi = Speed of the Taxi x Time

 = Y x 7

Distance covered by Bus = Speed of the Bus x Time

  = X x 8

 Total Distance covered

=> 8X + 7Y = 785   ------- (ii)

Solving (i) & Eq(ii) we get:

9X + 4Y = 670      

8X + 7Y = 785      

On solving for X and Y we get,

 => X = 50 km/hr

From (ii) we get;

8X + 7Y = 785

8(50) + 7Y = 785

=> 7Y = 785 - 400

=> 7Y = 385

=> Y = 55 km/hr

Therefore,

The Speed of the bus X= 50 kmph

The Speed of the taxi Y = 55 kmph