Paul decided to ride his bicycle across the country during h

Paul decided to ride his bicycle across the country during his 3-month summer vacation. The route he took from Washington, DC to Portland, Oregon, covered a total of 3480 miles. To keep his mind occupied during some of the long flat stretches of countryside, he often did algebra problems in his head. One day, for example, he determined that his distance from his starting point was exactly 90 miles more than twice the distance remaining until the finishing point. How far was Paul from the finishing point of his journey when he made that calculation? Start your work by defining the unknown quantities in terms of a variable. and write a complete answer, including units. Show check if applicable

Solution

Total distance traveled by paul = 3840 m

d = 3840 miles

Now suppose at the time of calculation paul had traveled = d1

remaining journey = d2

So,

d1 + d2 = 3840 miles

And

d1 = 90 + 2*d2

So,

d1 + d2 = 3840

d1 - 2*d2 = 90

Subttracting both equations:

3*d2 = 3840 - 90 = 3750

d2 = 3750/3 = 1250 miles

d1 = 3840 - 1250 = 2590 miles

Solution check

d1 = 90 + 2*d2

2590 = 90 + 2*1250