 Hi, and how are you all today? The question says a plane left 30 minutes later than the scheduled time and in order to reach its destination 1500 kilometer away in time it has to increase its speeds by 250 kilometer per hour from its usual speed find its usual speed So let's proceed with the solution here let The usual speed Be equal to x kilometer per hour right now the distance That needs to be traveled is 1500 kilometer so time taken to travel Will be equal to distance upon speed that is 1500 upon x hours right now Time taken to cover 1500 kilometer by increased speed That is x plus 250 kilometer per hour Will be equal to 1500 upon x plus 250 hours right now Further we are given from the question It says that a plane left 30 minutes later Then the scheduled time and it is reaching the destination in time. So that means We can say that X upon sorry 150 upon Sorry again 1500 upon x minus 1500 upon x plus 250 Is equal to 30 minutes that is half an hour right now what we need to do further is we just need to solve This quadratic equation that will be formed Simplified now we'll open the brackets in the denominator also we have x square plus 250 x after opening the bracket is equal to 1 by 2 further implies x square plus 250 x is equal to 250 into 1500 into 2 that is 75 0000 That further implies x square plus 250 x minus 75 0000 is equal to 0 now splitting the middle term we have plus 1000 x minus 750 x minus 75 0000 is equal to 0 so we have x Plus thousand as one of the factors and x minus 750 as one of the factors This implies the value of x is minus thousand or Equal to 750 since distance cannot be Sorry speed cannot be in negative hence The usual speed is Equal to 750 kilometer per hour Right, so this is the required answer to the question. Hope you understood it well enjoyed it to have a nice day