Question

Two trains leave a railway station at the
same time. The first train travels due west
and the second train travels due north. The
first train travels 10 km/h faster than the
second train. If after two hours, they are
100 km apart, find the average speed of
each train.
​

Answer 1

Step-by-step explanation:

the first train is moving with more speed than the second train.

the speed of the first train=d/t

Answer 2

$\huge \sf \color{purple}{\underline{\underline{Answer}}} :$

Speed of first train is 20 Km/h and speed of 2nd train is 15 Km/h

$\huge \sf \color{purple}{\underline{\underline{Solution}}}:$

➣ Let the 2nd train travel at X km/h

➣Then, the speed of a train is (10 +x) Km/hour.

➣ let the two trains live from station M.

➣ Distance travelled by first train in 2 hours

$\sf \boxed{\colorbox{skyblue}{Distance=speed×time}}$

= MA = 2(x+10) Km.

➣ Distance travelled by second train in 2 hours

= MB = 2x Km

$\sf \color{brown}{By \: Phythagoras \: theorem }$ AB²= MB²+MA²

⟹ 100²=(2(x+10)²+(2x)²

⟹ 1000 = (2x+10)² + 4x²

⟹10000=8x²+80x+400

⟹−8x²−80x+9600=0

⟹-8(x²+10x+1200)=0

⟹(x−30)(x+40)=0

⟹ x-30=0 OR x+40 =0

$\sf \boxed{\colorbox{lightgreen}{x=30 \: or \: -40}}$

Taking x = 30 , the speed of second train is 30 Km/h and speed of first train is 45 Km/h