A red candle is 8 inches tall and burns at a rate of 7/10 inch per hour. A blue cans is 6 inches tall and burns at a rate of 1/5 inch per hour. After how many hours will both candles be the same height

It would take 4 hours for both candles to be the same height

Step-by-step explanation:

Total time (t) for red candle to be same height (h) can be expressed as;

Final height after time t=Initial height-rate per hour

where;

Final height after time=h

Initial height=8 inches

Rate per hour=rate*time = (7/10) * t=0.7t

Substituting;

h=8-0.7t

Total time (t) for blue candle to be same height (h1) can be expressed as;

Final height after time t=Initial height-rate per hour

where;

Final height after time=h1

Initial height=6 inches

Rate per hour=rate*time = (1/5) * t=0.2t

Substituting;

h1=6-0.2t

Since h=h1

8-0.7t=6-0.2t

8-6=0.7t-0.2t

0.5t=2

t=2/0.5

t=4 hours

It would take 4 hours for both candles to be the same height