Question

Graham is hiking at an altitude of 14,040 feet and is descending 50 feet each minute.Max is hiking at an altitude of 12,500 feet and is ascending 20 feet each minute.How many minutes will it take Graham and Max to meet at the same altitude?

Answer 1

`\text{Hello there!}\\\\\text{Turn the statements into equations:}\\\\\text{Graham:}\\\\y=-50x+14,040\\\\\text{Max:}\\\\y=20x+12,500\\\\\text{We need to find when they will meet at the same altitude, so solve both}\\\text{of the equations together}\\\\-50x+14,040=20x+12,500\\\\\text{Subtract 20x from both sides}\\\\-70x+14,040=12,500\\\\\text{Subtract 14,040 from both sides}\\\\-70x=-1,540‬\\\\\text{Divide both sides by -70}\\\\x=22\\\\\boxed{\text{Answer: 22 minutes}}`