Jordan leaves his house and rides his bike at 10mi/h.After he goes 4 miles,his brother Tim leaves the house and rides in the same direction at 12mi/h.If heir rates stay the same,will Tim ever catch up

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Yes, tim will catch up.

As with all similar word problems, first create an equation from the given information.D = Distance (in miles)V = Velocity (in miles/hour)T = Time (in hours)We know that Distance = Velocity * Time(or simply: D=VT)The question asks: Will Tim and Jordan ever be the same distance (D) from the house at the same time (T)? Let's come up with formulas for the distance of Jordan and Tim from their house. We'll start the clock at 0 hours when Tim leaves.Jordan's distance:D = (10m/h * T) + 4mTim's distance:D = 12m/h * TWe can check to see if Tim will ever catch up by testing our equations at different times.At T = 0h: Jordan is 4 miles, Tim is 0 milesAt T = 1h: Jordan is 14m, Tim is 12mAt T = 2h: Jordan is 24m, Tim is 24mAt T = 3h: Jordan is 34m, Tim is 36mWe find that 2 hours after Tim leaves, he's caught up to Jordan. A manual calculation might look like this:(12m/h * T) = (10m/h * T) + 4m(12m/h * T) - (10m/h * T) = 4m(12m/h - 10m/h) * T = 4m2m/h * T = 4mT = 2h