motorcycle race 1 lape=750m. at the start gina sets off 4 sec. after tom but drives the motorcycle 3.5m/s fasteran finishes in 2.5sec. sooner then tom. at what speed was gina driving?

To find the speed at which Gina was driving, we first need to calculate the time it took for both Gina and Tom to complete the race.

Let's assign the following variables:
- Gina's time: t (in seconds)
- Tom's time: t + 4 (since Gina sets off 4 seconds after Tom)

We know that the distance they both travel is equal to one lap, which is 750m.

For Gina:
Distance = Speed * Time
750 = Speed_Gina * t

For Tom:
Distance = Speed * Time
750 = Speed_Tom * (t + 4)

Since Gina drives the motorcycle 3.5 m/s faster than Tom, we can express Gina's speed in terms of Tom's speed:
Speed_Gina = Speed_Tom + 3.5

Now we can solve the equations:

750 = Speed_Gina * t
750 = (Speed_Tom + 3.5) * (t + 4)

First, let's rewrite the second equation:
750 = (Speed_Tom * t) + (Speed_Tom * 4) + (3.5 * t) + (3.5 * 4)

Simplifying further:
750 = Speed_Tom * t + 4 * Speed_Tom + 3.5 * t + 14

Combining like terms:
750 = (Speed_Tom + 3.5) * t + 4 * Speed_Tom + 14

Now, we can substitute the value of Speed_Gina into the equation:
750 = (Speed_Tom + 3.5) * t + 4 * Speed_Tom + 14

Let's simplify and solve for t:

750 = (Speed_Tom + 3.5)t + 4Speed_Tom + 14
750 = Speed_Tom * t + 3.5 * t + 4 * Speed_Tom + 14
750 = (t + 3.5)Speed_Tom + 3.5t + 14

Rearranging the equation:
750 - 14 = (t + 3.5)Speed_Tom + 3.5t
736 = (t + 3.5)Speed_Tom + 3.5t

Now, we have one equation with two variables, which means we need another equation to help solve for t and Speed_Tom.

We are given one more piece of information: Gina finishes the race 2.5 seconds sooner than Tom. This can be expressed as:
t + 2.5 = (t + 4) - 2.5

Simplifying:
t + 2.5 = t + 1.5

Subtracting t from both sides:
2.5 = 1.5

This equation is not possible, which tells us there is an error in the information provided. Please double-check the given information and ensure accurate values are provided.