A lamp lighter has to light 100 gas lamps He takes one and half minutes to go from one - Maths - Arithmetic Progressions

Question

A lamp lighter has to light 100 gas lamps He takes one and half
minutes to go from one lamp post to the next Each lamp burns 10
cubic feet of gas per hour How many cubic feet of gas has been
burnt by 8 30pm, if he lights the first/last lamp at 6pm

Harleen Birdi · Accepted Answer

Each lamp burns 10 cubic ft of gas/hr $\Rightarrow Each lamp burns \frac{10}{60} cubic ft/min = \frac{1}{6} cubic ft /minute$ Number of hours from 6 p m to 8:30 = 2 5 hrs = 150 minutes He takes 1 5 minutes to go from one lamp to another So, 1st lamp will burn for 150 minutes 2nd lamp will burn for (150 â€“ 1 5) min = 148 5 3rd lamp will burn for (148 5 â€“ 1 5) min = 147 $∴ Gas used = \frac{1}{6} [150 + 148 5 + 147 + + 1 5] = \frac{1}{6} \times \frac{100}{2} (150 + 1 5) [\begin{array}{l} ∵ (150 + 148 5 + 1 5) form or AP with common difference 1 5 and \\ number of terms = 100 \end{array}]$ = 1262 5 cubic feet

A lamp lighter has to light 100 gas lamps. He takes one and half minutes to go from one lamp post to the next. Each lamp burns 10 cubic feet of gas per hour. How many cubic feet of gas has been burnt by 8.30pm, if he lights the first/last lamp at 6pm