Rational Expression Word Problem

[msimard8]

In a motorcycle race, one lap of the course is 650m. At the start of the race, Genna sets off 4 seconds after Tom does, but she drives her motorcycle 5m/s faster and finishes the lap 2.5 seconds sooner than he does.

a) Find the speed at which each of them is driving.

b) Find the tim etaken by each of them to cover the distance.
How I started this problem

Let x be Genna's time if she started at the same time

Genna
time =x
distance =650
speed = 650/x

Tom

time = x +2.5
distance =650 m
speed = x +2.5

then i did 650/x - 650/x+2.5 = 5m/s

this generated the wrong answers

here are the correct answers

a)Tom 20m/s Genna 25.0m/s
b) Tom 32.5 s Genna 6s

Help

thanks

 

[Hootenanny]

You forgot to take into account that Genna started 4 seconds after Tom. Also Tom's speed is not given by;

speed = x +2.5

~H

 

[Architeuthis Dux]

I would approach this problem by first understanding the given information and the relationship between the variables involved. In this case, we are given the distance of the lap (650m) and the time difference between Genna and Tom (4 seconds).

To find the speed at which each of them is driving, we can use the formula: speed = distance/time. Let's assume Tom's speed is represented by v and Genna's speed is represented by v+5 (since Genna drives 5m/s faster than Tom).

a) Tom's speed (v) can be calculated as 650/(x+4), where x is the time taken by Tom to complete the lap. Similarly, Genna's speed (v+5) can be calculated as 650/x.

To solve for x, we can equate the two expressions and solve for x. This gives us x=13 seconds. Therefore, Tom's speed is 650/17 = 38.24 m/s and Genna's speed is 650/13 = 50 m/s.

b) To find the time taken by each of them to cover the distance, we can plug in the values of x (13 seconds) and x+4 (17 seconds) in the respective speed equations. This gives us Tom's time as 13 seconds and Genna's time as 6 seconds.

In conclusion, I would advise double-checking your equations and making sure all the variables are correctly represented before solving the problem. It is also important to understand the relationship between the given information and the variables involved in order to approach the problem correctly.