Rate Time and Distance?

Question

Rate Distance and Time?
Marcus rode his bicycle to the park at 14 mph. He rode from the park at 21 mph. If the total trip took 3 1/2 hours, how far was it to the park?

Answer 1

x-distance to park
x/14+x/21=3.5 multiply both sides by 42
3x+2x=147
5x=147 divide by 5
x=29.4 miles

Answer 2

These questions are tricky and must be solved using algebra or if you are good with spreadsheets that will work as well. THE CORRECT ANSWER IS THAT THE DISTANCE TO THE PARK IS 29.4 miles. It took Marcus 2.1 hours to travel to the park and 1.4 hours to return. Interestingly you will notice that the time required to travel the distance is proportional to the rate. The ratio for both is 2:3.

In the previous response the assumption about the distance being the same is correct but they made the mistake of trying to average the rates or travel. As an example, If you travel 100 miles in one hour and the next 100 miles takes ten hours, you have traveled 200 miles in 11 hours. The first 100 miles was done at 100 MPH and the second was done at 10 MPH. So, what was the average speed?

The average is 200 divided by 11 (this gives you 18.18 miles per hour). YOU CANNOT ADD THE 100 MPH WITH THE 10 MPH AND DIVIDE BY TWO. This would result in an average of 55 MPH which is obviously wrong.

Answer 3

Let

x/14 = the speed of the bicycle to the park

x/21 = The speed of the bicycle from the park

3.5 = Total time to and from the park

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The equation

x/14 + x/21 = 3.5

42(x/14) + 42(x/21) = 42(3.5)

3x + 2x = 147

5x = 147

5x/5 = 147/ 5

x = 29.4 Miles

The answer is: The distance to the park is 29.4 Miles

Insert the x value into the equation

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Check

x/14 + x/21 = 3.5

29.4/14 + 29.4/21 = 3.5

2.1 + 1.4 = 3.5

3.5 = 3.5

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Answer 4

assuming he went the same route both ways:
it took him 3/2 times as long going 14 mph, because 21/14 = 3/2. becuase of this we know that the total time was 3/2 + 1 = 5/2 of the time it took going at 21 mph. so we know that 5/2*(x/21) = 3.5 and we know from that that x/21 = 1.4 or x = 29.4 miles

we can check this answer by doing 29.4/14 + 29.4/21 = 3.5
doing the math on that we get 2.1 + 1.4 = 3.5

so we know that 29.4 miles is the correct answer

Answer 5

logically you should be able to figure this out.....
1. the distance there and back are equal, therefore you can get the average speed for both departing and returning:
14 mph +21 mph/2 = 17.5 mph average.
2. both trips took 3.5 hrs. therefore 17.5 x 3.5= 61.25 miles round trip
3. 61.25/2 = 30.625 miles is the distance to the park

Answer 6

Time(educate) = Distance(educate) / speed(educate) Time(freight) = Distance(freight) / speed(freight) this is stated that they are equivalent, so: Distance(educate) / speed(educate) = Distance(freight) / speed(freight) 520 / (x + 25) = 320 / x remedy for x: speed(freight) = x = 40mph speed(educate) = x + 25 = 65mph

Answer 7

You got the basic idea;

rt=d,

Some significant fraction of the algebra problems that you work on involve this relationship.

Answer 8

average speed=1/2(v-u)=17.5mph
total distance=17.5*3.5=61.25m
distance of park=61.25/2=30.625m