Question

Anil’s friend suggested that he should jog and swim regularly to burn the excess calories. Anil started swimming for 180 minutes and jogging for 120 min in a week and lost 2400 calories. In the next week he lost 3200 calories by swimming for 2 hours and jogging for 4 hours. Represent the above statements in the form of linear equations and solve them algebraically to find the calories burnt in swimming in an hour and jogging in an hour.

Answer 1

Dear student,

Let the calories burnt by swimming in an hour be x.

And let the calories burnt by jogging in an hour be y.

$$\begin{gathered} \mathrm{According}\mathrm{to}\mathrm{question},\mathrm{the}\mathrm{system}\mathrm{of}\mathrm{linear}\mathrm{equations}\mathrm{is} \\ 3\mathrm{x}+2\mathrm{y}=2400.....\left(1\right) \\ 2\mathrm{x}+4\mathrm{y}=3200....\left(2\right) \\ \mathrm{Multiply}\left(1\right)\mathrm{by}2,\mathrm{we}\mathrm{get} \\ 6\mathrm{x}+4\mathrm{y}=4800....\left(3\right) \\ \mathrm{Subtracting}\left(2\right)\mathrm{from}\left(3\right),\mathrm{we}\mathrm{get} \\ 6\mathrm{x}-2\mathrm{x}=4800-3200 \\ \Rightarrow 4\mathrm{x}=1600 \\ \Rightarrow \mathbf{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{400} \\ \mathrm{Now},\mathrm{put}\mathrm{x}=400\mathrm{in}\left(1\right),\mathrm{we}\mathrm{get} \\ 3\times 400+2\mathrm{y}=2400 \\ \Rightarrow 1200+2\mathrm{y}=2400 \\ \Rightarrow 2\mathrm{y}=1200 \\ \Rightarrow \mathbf{y}\mathbf{}\mathbf{=}\mathbf{}\mathbf{600} \end{gathered}$$

Thus, calories burnt by swimming in an hour = 400 calories

and calories burnt by jogging in an hour = 600 calories

Regards