Question 1005032: It is thought by many in the scientific community that ants navigate to and from their nests by way of an internal pedometer. In other words, ants count how many steps they take away from their nest and count the same amount of steps to return. If an ant covers a distance of 2.5 mm per step, then how many steps will the ant count if he leaves his nest and walks to a food source 1.4 m away?
Scientists have tested this hypothesis by putting small stilts made from pig’s bristles on the end of ants’ legs. The scientists found that when the length of the ants’ legs was extended, the ants would overshoot, or go past, their destination. Scientists believe this is because the ants would take the same number of steps but with a longer stride (distance per step) due to the increased leg length. The ant from the previous question had stilts attached to his legs once he reached the food source. On his journey back to the nest, he walked 0.7 m past his destination. By how many millimeters was his stride extended by the stilts? Express your answer as a decimal to the nearest hundredth.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 1 meter = 1000 millimeters.
normal stride is 2.5 millimeters per step.
food source is 1.4 meters away * 1000 = 1400 millimeters away.
1400 millimeters / 2.5 millimeters = 560 steps at 2.5 millimeters per step.
with stilts, the ant oversteps the distance by .7 meters.
1.4 meters + .7 meters = 2.1 meters = 2100 millimeters.
2100 millimeters / 560 steps = 3.75 millimeters per step.
3.75 millimeters minus 2.5 millimeters = 1.25 millimeters.
the length of the ant's step was increased by 1.25 millimeters.
instead of covering 2.5 millimeters per step, the ant was covering 3.75 millimeters per stride.
2.5 * 560 steps = 1400 millimeters = 1.4 meters.
3.75 * 560 steps = 2100 millimeters = 2.1 meters.
2.1 meters is .7 meters more than 1.4 meters.
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