Question

solve:two automobiles start out at the same time from cities 595 kilomete apart.If the speed of one is 8/9 of the speed of the other & if they meet in 7 hours,what is the speed of each.

Answer 1

Let the speed of one automobile (A)= x km/h
speed of other automobile (B) = 8x/9 km/h
total time = 7 hours
total distance travelled = 595 km

distance travelled by A = 7x km  (velocity×time)
distance travelled by B = 7×(8x/9) km = 56x/9

Total distance = $7x+ \frac{56x}{9}=595$

⇒$\frac{63x+56x}{9}=595$

⇒$\frac{119x}{9}=595$

⇒$119x = 9*595$

⇒x = $\frac{9*595}{119} =45km/h$ (speed of A)

$\frac{8x}{9}= \frac{8*45}{9}=40km/h$ (speed of B)

Answer 2

$\sf\bold{\underline{\pink{SOLUTION}}}$

Let the speed of one automobile (A) = x km/h

Speed of other automobile (B) = $\sf{\dfrac{8}{9}x}$ km/h

Total Time Taken = 7 hours

Total distance travelled = 595 km

$\sf\small\orange{\fbox{Distance \:Traveled \:by\: A\: +\: Distance\: traveled \:by\: B = 595 km}}$

$⇒\sf{7x + 7 ×\dfrac{8}{9}x = 595 \:km}$

$⇒\sf{x + \dfrac{8}{9}x = 85}$

$⇒\sf{\dfrac{17}{9} x = 85}$

$⇒\sf{x = \dfrac{85 × 9}{17}}$

$⇒\sf\pink{\fbox{x = 45 km/h}}$

Speed of Automobile (A) = x = 45 km/h

Speed of Automobile (B) = $\sf{\dfrac{8}{9}x}$ = 40 km/h