Question

The relationship between speed, distance, and time can be modeled using this equation, where: s = speed
, d = distance, and t = time.
s = d/t
Part 1
You're on a road trip with friends, but you can't see the GPS. You want to calculate how many miles you will drive on each highway.

Rewrite the equation so it is solved for d.
Show all steps.
Part 2
You just merged onto the PA turnpike, and the GPS started "Continue for 90 minutes." Your friend follows the speed limit of 70 mph and maintains a constant speed
Using your equation from Part 1, determine how many miles you will travel on the turnpike. Show all your work.

*Speed is in miles per hour. Make sure your time is converted to the same unit!*
Part 3
Is it possible to rewrite the equation again to easily calculate the time based on distance and speed? Explain

Answer 1

Part 1 — solve for d:
1. Start with s = d/t.
2. Multiply both sides by t to eliminate the denominator: s·t = (d/t)·t.
3. Simplify the right side: s·t = d.
4. So d = s·t.

Part 2 — how many miles in 90 minutes at 70 mph:
1. Convert time to hours: 90 minutes = 90/60 = 1.5 hours.
2. Use d = s·t: d = 70 mph · 1.5 h = 105 miles.
Answer: 105 miles.

Part 3 — solve for time:
Yes. From s = d/t, multiply both sides by t: s·t = d. Divide both sides by s (s ≠ 0): t = d/s.
Note: t is undefined if s = 0 (unless d = 0, in which case any t gives d = 0). Units: with d in miles and s in mph, t is in hours.