a. A car travels a distance of 112 km at an average speed of 70 km/h. it then travels a further 60 km at an average speed of 50 km/h. Calculate, for the entire journey, the total time taken.
b. if \(\frac{x}{y}\) = 2 and \(\frac{y}{z}\) = 3, find the value of \(\frac{ x + y}{y + z }\)
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, \(\frac{ x + y}{y + z } = \frac{9}{4}\)