Question

Anish started his journey by car at 10:00 am from Lucknow to Delhi. Manav also
started his journey by a car which is 12 km/h faster, from Delhi to Lucknow at the same time along the same route.
After 4½hrs. the distance between them is 29 km.
Find the speed with which each car is travelling, if the distance between Lucknow and Delhi is 497 km.​

Answer 1

$\sf\underline\red{SOLUTION :}$

Let's assume the speed of Anish's car be x km/hr.

Then, Speed of Manav's car will be (x + 12) km/hr.

$\bullet{\text{\sf{Distance covered by Anish in 4}}}\sf\dfrac{1}{2}hr. :$

$\mapsto\sf{4}\dfrac{1}{2}\times{x km}$

$\bullet{\text{\sf{Distance covered by Manav in 4}}}\sf\dfrac{1}{2}hr. :$

$\mapsto\sf{4}\dfrac{1}{2}\times{(x+12)km}$

${\text{\sf{\pink{Here, (Distance = Speed + Time)}}}}$

Now,

Distance travelled by Anish + Distance travelled by Manav + 29 = Total distance (i e. 497 km)

A/Q

$\leadsto\sf{4}\dfrac{1}{2}x +\sf{4}\dfrac{1}{2}(x+12)+29=497$

$\leadsto\sf\dfrac{9}{2}x +\dfrac{9}{2}x+54+29=497$

$\leadsto\sf{9x=497-83}$

$\leadsto\sf{9x=414}$

$\leadsto\sf{x=}\dfrac{\cancel{414}^{46}}{\cancel{9}^1}$

$\leadsto\sf{x=46\ km/h}$

∴ The speed of Anish's car (x) = 46 km/h.

Thus, Speed of Manav's car (x + 12) = 46+12 = 58 km/h.