Question

Abdul travelled 300km by trains and 200km by taxi, it took 5 hours 30 minutes.but if he travels 260km by train and 240 km by taxi,he takes 6 minutes longer.Find the speed of the train and that of the taxi.

Help please :)​

Answer 1

Answer:

ABDUL TRAVELLED BY TRAIN =300 KM

HE TRAVELLED BY TAXI =200 KM

TIME TAKEN = 5 HR 30 MIN=5+3×1/60=5.5 HR.

NOW AGAIN IF HE TRAVELLED,

BY TRAIN 260 KM AND 240 KM BY TAXI THEN TIME TAKEN IS 6 MIN LONGER=6×1/60=0.1 HR.

WE GET,

TOTAL DISTANCE COVERED BY TRAIN=300+260=560 KM

TOTAL TIME TAKEN = 5.5+0.1=5.6 HR

SPEED OF TRAIN = DISTANCE/TIME

=560/5.6=100 KM / H.

TOTAL DISTANCE COVERED BY TAXI =200+240=440 KM.

TOTAL TIME TAKEN = 5.6 HR.

SPEED OF TAXI= 440/5.6=78 KM/H

NOW RATIO OF SPEED OF TRAIN TO SPEED OF TAXI:

100/78=50:39

Answer 2

Answer:

$\bigstar{\bold{Speed\:of\:train=100\:km/hr}}$

$\bigstar{\bold{Speed\:of\:taxi=80\:km/hr}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• If Abdul travelled 300 km by train and 200 km by taxi, it takes 5 hours and 30 minutes.
• If Abdul travelled 260 km by train and 240 km by taxi, he takes 6 minutes longer

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Speed of the train
• Speed of the taxi

$\Large{\underline{\underline{\bf{Solution:}}}}$

➣ Let speed of train be x km /hr

➣ Let speed of taxi be y km/hr

➣ We know that

    Time = Distance/Speed

➣ Hence by first case,

    $\dfrac{300}{x} + \dfrac{200}{y} = 5+ \dfrac{30}{60}$

    $\dfrac{300}{x}+\dfrac{200}{y}=\dfrac{11}{2}-------equation\:1$

➣ By second case,

    $\dfrac{260}{x}+\dfrac{240}{y}=\dfrac{11}{2}+\dfrac{6}{60}$

    $\dfrac{260}{x}+\dfrac{240}{y}=\dfrac{56}{10}-----equation\:2$

➣ Now let 1/x = p and 1/y = q

➣ Hence equation 1 and 2 changes to,

    300p + 200q = 11/2-------equation 3

    260p + 240q = 56/10------equation 4

➣ Multiply equation 3 by 6 and equation 4 by 5

    1800p + 1200q = 33

    1300p + 1200q = 28

➣ Solving by elimination method,

    500p = 5

           p = 1/100

➣ We know that p = 1/x, hence x = 100

➣ Hence speed of train is 100 km/hr

$\boxed{\bold{Speed\:of\:train=100\:km/hr}}$

➣ Substitute the value of p in equation 3

    300/100 + 200q = 11/2

    3 + 200q = 11/2

    200q = 11/2 - 3

    200q = 5/2

            q = 5/2 × 1/200

            q = 1/80

➣ We know that q = 1/y, hence y = 80

➣ Hence speed of the taxi is 80 km/hr

$\boxed{\bold{Speed\:of\:taxi=80\:km/hr}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

A linear equation in two variables can be solved by

• Substitution method
• Elimination method
• Cross multiplication method