Chain rule

Question

If 9 engines consume 24 metric of coal , when each is working a 8 hours a day ;

how much coal will required for 8 engines each running 13 hours a day it is been given that 3 engines of former type consume 4 engines of latter type ?

Comments

i got proportionality , but my answer are not matching

Answer 1

9 engines consume 24 metric of coal , when each is working a 8 hours a day

So, per hour consumption of one former engine $ = \frac{24}{8 \times 9} = \frac{1}{3}.$

3 engines of former type consume 4 engines of latter type 

So, the newer engine consumes less by a factor of $\frac{3}{4}.$

how much coal will required for 8 engines each running 13 hours a day

Will be $8 \times 13 \times \frac {1}{3} \times \frac{3}{4} = 26.$