Question

two cities p and q are 1200 km apart. At 9am a volvo leaves P and Q and an Armada leaves Q for P. volvo covers one third the distance at a speed of 80km/hr, half the remaining distance at 100 km/hr and the rest at 120km/hr. Armada completes the joirney by travelling at 80km/hr, 100km/hr and 120km/hr respectively for equal time intervals. when and where will the two vehicles cross each other?

Answer 1

I don't know what you have wrote

Answer 2

Answer:  at 3:08 pm  they will cross each other.

Step-by-step explanation:

Since we have given that

Distance between two cities = 1200 km

One third of the distance covered at a speed of 80 km/hr.

$\frac{1}{3}\times 1200\\\\=400\ km$

Time taken is given by

$Time=\frac{Distance}{Speed}=\frac{400}{80}=5\ hours$

Remaining distance is given by

$1200-400=800$

Time taken is given by

$Time=\frac{Distance}{Speed}=\frac{400}{80}=5\ hours$

Half the remaining distance covered at a speed of 100 km/hr

$\frac{1}{2}\times 800\\\\=400\ km$

Time taken is given by

$Time=\frac{Distance}{Speed}=\frac{400}{100}=4\ hours$

Rest of the distance covered at a speed of 120 km /hr.

$800-400=400\ km$

Time taken is given by

$Time=\frac{Distance}{Speed}=\frac{400}{120}=\frac{10}{3}\ hours$

First we find the average speed :

$Speed=\frac{Distance}{Time}$

$Speed=\frac{1200}{5+4+\frac{10}{3}}\\\\Speed=\frac{1200}{9+\frac{10}{3}}\\\\Speed=\frac{1200\times 3}{27+10}=\frac{3600}{37}=97.29\ km/hr$

Now, Speed at which Armada covers is given by

$Let\ \frac{x}{80}=k=\frac{y}{100}=\frac{120}{k}\\\\x=80k,y=100k,z=120k\\\\\frac{1200}{\frac{x}{80}+\frac{y}{100}+\frac{z}{120}}\\\\=\frac{1200}{3k}\\\\=\frac{400}{k}$

now,

$x+y+z=1200\\\\80k+100k+120k=1200\\300k=1200\\\\k=\frac{1200}{300}=4$

so, it becomes,

$\frac{400}{4}=100\ km/hr$

Now, they cross each other where, volvo covers 'd' distance and Armada covers '1200-d' distance.

$\frac{d}{\frac{3600}{37}}=\frac{1200-d}{100}\\\\100d=\frac{3600}{37}\times (1200-d)\\3700d=3600(1200-d)\\\\d=591.78\ km\hr$

time taken is given by

$t=\frac{1200-d}{100}\\\\t=\frac{1200-591.7}{100}\\\\t=6.08\ hours$

Hence, at 3:08 pm  they will cross each other.