Wilfred and Wendy have a long distance bike race. Wilfred rides at 20km/h and has a 2 hour head start. Wendy travels at 28 km’h. How long does it take for Wendy to catch up to Wilfred?
To work this problem out, use algebraic form.
t is the time to catch up (Wendy's time)
... she catches up when they have traveled the same distance
... his travel time is two hours longer
20 * (t + 2) = 28 * t
To solve this problem using algebraic form, let's first define the variables.
Let t be the time it takes for Wendy to catch up to Wilfred.
Since Wilfred has a 2-hour head start, we can express his distance traveled as 20 * (t + 2). (20 km/h multiplied by the time (t + 2) since he started 2 hours earlier).
Similarly, Wendy's distance traveled can be represented as 28t (28 km/h multiplied by the time t).
We know that when Wendy catches up to Wilfred, their distances traveled will be equal. Therefore, we can set up the equation:
20 * (t + 2) = 28t
Now let's solve this equation step by step:
20t + 40 = 28t (Distributing 20 to (t + 2))
40 = 8t (Subtracting 20t from both sides)
5 = t (Dividing both sides by 8)
Therefore, it will take Wendy 5 hours to catch up to Wilfred.