Algebra II

posted by .

can you help answer this question please; four algebra formulas for Amadeus traveled 760 miles in twice the time it took his nemesis Salieri to travel 220 miles. if Amadeus"s rate exceeded Salieri's by 40 miles per hour, what were the rate and time for each man?

  • Algebra II -

    Two equations:

    1.) Amadeus

    760miles=R1*T1

    2.) Salieri

    220miles=R2*T2

    Let R1=R2+40

    and

    Let T1=2*T2

    Substitute into equations and solve:

    760miles=(R2+40)*(2*T2)

    Solving for T2:

    380 miles/(R2+40)=T2

    Plug into equation 2 and solve for R2:

    220 miles=R2*[380 miles/(R2+40)]

    220 miles*R2+8,800 miles=R2*380 miles

    160 miles*R2=8,800 miles

    R2=55 miles/hr

    Solve for other variables using the two equations or the T and R equations:

    =================================

    R1=R2+40=55+40=95 miles/hr

    T2=220 miles/R2=R=220 miles/55=4 Hr

    T1=2*T2=2*(4)=8 Hr

    R2=55 miles/hr

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    The relationship between the speed of travel and the distance traveled can be described by the equation d=rt where d = distance traveled in miles, r = speed (or rate) of travel in miles per hour, and t = time traveled in hours. Graph …
  2. math

    explain how to write 20 miles divided by 4 hours as a unit rate If that's distance traveled per unit of time it would be 20miles per 4 hrs but since it's usually compared per hour... 20/4= 5 miles so every hour you travel 5 miles and …
  3. algebra

    DRT problem A bicyclist travels 20 miles per hour faster than a walker. The cyclist traveled 25 miles in the time it took the walker to walk 5 miles. Find their speeds.
  4. algebra

    A train can travel 280 miles in the same time that it takes a car to travel 140 miles. If the train's rate is 40 miles per hour faster than the cars, find the average for each.
  5. Algebra

    Ben traveled by car at an average speed of 29 miles per hour. Then, he traveled by motorcycle at an average speed of 53 miles per hour. In total, he traveled 333 miles for 9 hours. How many minutes did Ben travel by motorcycle?
  6. Algebra Help

    A motorist was to travel from town A to town B, a distance of 80 miles. He traveled the first 24 miles at a certain rate; traffic then increased and for the next 6 miles he averaged 10 miles per hour less than his original speed; then …
  7. Math- Multi-step word problems

    A canoe in still water travels at a rate of 10 miles per hour. The current today is traveling at a rate of 3 miles per hour. If it took an extra hour to travel upstream, how far was the trip one way?
  8. Trigonometry- Help!

    After one hour in flight, an airplane is located 200 miles north and 300 miles west of the airport. What is the magnitude of the plane's velocity?
  9. Math

    Which ratio is equivalent to 4/16 A. 2:4•• B. 6 to 20 C. 8:32 D. 12 to 64 Write the ratio as a unit rate. 286 miles in 5 1/2 hours A. 36 miles per hour B. 52 miles per hour •• C. 57.2 miles per hour D. 114.4 miles per hour …
  10. algebra

    A boat can travel 38 mph in still water. If the boat can travel 100 miles with the current in the same time it can travel 80 miles against the current, find the rate of the current r in miles per hour.

More Similar Questions