1) A tractor wheel is 88 inches in circumference. How many complete turns will the wheel make in rolling one mile on the ground? (1 mile = 5,280 feet)
2) In the addition problem below, each letter represents a digit and different letters represent different digits. What four-digit number does D E E R represent?
+ R I D
D E E R
3) Alice and Betty run a 50-meter race and Alice wins by 10 meters. They then run a 60-meter race, and each girl runs at the same speed she ran in the first race. By how many meters will Alice win?
1) When the wheel makes one complete turn, it has rolled a distance of 88 inches. The number of turns equals 1 mile divided by 88 inches
(1 mile = 5280 feet = 5280 x 12 inches).
Dividing yields 5280 x 12 inches = 720
2) D in the sum DEER must be 1. The R in the second addend must be 9. It follows that E must be 0 and DEER represents 1009.
3) Method 1
Alice runs 50m in the same time that Betty runs 40m. Thus Alice runs 5m for every 4m that Betty runs. Therefore in the 60m race, Alice will run 12 x 5m or 60m, and Betty will run 12 x 4 = 48m. So Alice wins by 12m.
Since Alice wins the 50m race by 10m, Alice must gain 2m over Betty for every 10m that Alice runs. Therefore, in a 60m races, Alice will gain 6 x 2m or 12m.