a. A car travels a distance of 112 km at an average speed of 70

Explanation

a. The total time taken for the entire journey is the sum of time taken for each journey.

But Average speed = \(\frac { total distance covered}{ time taken}\)

then Time taken = \(\frac { total distance covered}{ time taken}\)

for the first journey(t1), d = 112km and speed = 70km/hr

\(t_1 = \frac{112}{70} = \frac{8}{5}\)hrs

for the second journey(t2), distance = 60km and speed = 50km/hr

\(t_2 = \frac{60}{50} = \frac{6}{5}\)hrs

Therefore, Total time taken = \( t_1 + t_2 = \frac{8}{5} + \frac{6}{5}\) = 2.8hrs.

b. if \(\frac{x}{y}\) = 2 , then x = 2y and if \(\frac{y}{z}\) = 3 then z = \(\frac{y}{3}\),

substituting, the values of x and z into \(\frac{ x + y}{y + z }\)

= \(\frac{2y + y}{y + \frac{y}{3}} = 3y\div\frac{4y}{3} = 3y\times\frac{3}{4y} = \frac{9}{4}\)

Therefore, \(\frac{ x + y}{y + z } = \frac{9}{4}\)