Question

A distance of 1200km is to be covered using both Train & Bus. If the first 240 km are covered by train and rest by bus, it takes 16 hr in all. However, if the train is used for 160 km more, it takes 40 min more for the entire journey. What is the speed of the train?

Answer 1

Given :  A distance of 1200km is to be covered using both Train & Bus.

If the first 240 km are covered by train and rest by bus, it takes 16 hr in all. However, if the train is used for 160 km more, it takes 40 min more for the entire journey.

To Find : What is the speed of the train?​

Solution:

Train Speed = T km/hr

Bus speed = B km/hr

Distance = 1200 km

By train = 240 km

by Bus  = 1200 - 240  = 960 km

Time taken  = 240/T  + 960/B  = 16

=> 15/T  + 60/B  = 1

By train = 160 km

by Bus  = 1200 - 160  =1040 km

16 hr 40 mins = 16  + 40/60  = 16 + 2/3  = 50/3 hrs

Time taken  = 160/T  +1040/B  = 50/3 hrs

=> 16/T  + 104/B  = 5/3

=>  48/T  + 312/B  =  5  

15/T  + 60/B  = 1 => 26 * 15/T  + 1560/B = 26

48/T  + 312/B  =  5  => 5*48/T + 1560/B  = 25

=> (390 - 240)/T  = 1

=> 150/T = 1

=> T = 150

Train Speed = 150 km/hr

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Answer 2

Answer:

To Find : What is the speed of the train?​

Train Speed = T km/hr

Bus speed = B km/hr

Distance = 1200 km

By train = 240 km

by Bus  = 1200 - 240  = 960 km

Step-by-step explanation:

Time taken  =   240/T  +   960/B  =   16

                     => 15/T  + 60/B  =  1  ------------ (a)

If the train is used for 160 km more.

Distance cover by train = 240 + 160 km

                                       = 400 km

Distance cover by bus = 1200 - 400 km

                                     = 800 km

it takes 40 min more for the entire journey.

16 hr 40 mins = 16  + 40/60  = 16 + 2/3  = 50/3 hrs

Time taken  =   400/T  +   800/B  =   50/3

                     => 40/T  +   80/B  =   5/3

                    =>  8/T  +   16/B  =   1/3 ------------ (b)

Now Comparing The equetation (b) and (a) we get,

8/T  +   16/B  =   1/3=>120/T  +   240/B  =   15/3   ------------ (b)

15/T  + 60/B  =  1  => 60/T  + 240/B      =      1      ------------ (a)

------------------------------------------------------------------------------------

                                                 =>  60/T = (15-12)/3

                                                 => 60/T = 1

                                                 => T = 60

Train Speed = 60 km/hr